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Wyświetlanie 1-15 z 19
Tytuł:
Differential Batalin-Vilkovisky algebras arising from twilled Lie-Rinehart algebras
Autorzy:
Huebschmann, Johannes
Powiązania:
https://bibliotekanauki.pl/articles/1207674.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
differential graded Lie algebra
twilled Lie-Rinehart algebra
Lie-Rinehart algebra
Batalin-Vilkovisky algebra
Gerstenhaber algebra
mirror conjecture
Calabi-Yau manifold
Lie bialgebra
Opis:
Twilled L(ie-)R(inehart)-algebras generalize, in the Lie-Rinehart context, complex structures on smooth manifolds. An almost complex manifold determines an "almost twilled pre-LR algebra", which is a true twilled LR-algebra iff the almost complex structure is integrable. We characterize twilled LR structures in terms of certain associated differential (bi)graded Lie and G(erstenhaber)-algebras; in particular the G-algebra arising from an almost complex structure is a (strict) d(ifferential) G-algebra iff the almost complex structure is integrable. Such G-algebras, endowed with a generator turning them into a B(atalin-)V(ilkovisky)-algebra, occur on the B-side of the mirror conjecture. We generalize a result of Koszul to those dG-algebras which arise from twilled LR-algebras. A special case thereof explains the relationship between holomorphic volume forms and exact generators for the corresponding dG-algebra and thus yields in particular a conceptual proof of the Tian-Todorov lemma. We give a differential homological algebra interpretation for twilled LR-algebras and by means of it we elucidate the notion of a generator in terms of homological duality for differential graded LR-algebras.
Źródło:
Banach Center Publications; 2000, 51, 1; 87-102
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Varieties of topological groups, Lie groups and SIN-groups
Autorzy:
Hofmann, Karl
Morris, Sidney
Stroppel, Markus
Powiązania:
https://bibliotekanauki.pl/articles/966844.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
pro-Lie group
varieties of topological groups
IN-group
SIN-group
Lie group
Opis:
In this paper we answer three open problems on varieties of topological groups by invoking Lie group theory. We also reprove in the present context that locally compact groups with arbitrarily small invariant identity neighborhoods can be approximated by Lie groups
Źródło:
Colloquium Mathematicum; 1996, 70, 2; 151-163
0010-1354
Pojawia się w:
Colloquium Mathematicum
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Left-covariant differential calculi on $SL_{q}(N)$
Autorzy:
Schmüdgen, Konrad
Schüler, Axel
Powiązania:
https://bibliotekanauki.pl/articles/1342724.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
quantum Lie algebra
noncommutative differential calculus
Opis:
We study $N^{2} - 1$ dimensional left-covariant differential calculi on the quantum group $SL_q(N)$. In this way we obtain four classes of differential calculi which are algebraically much simpler as the bicovariant calculi. The algebra generated by the left-invariant vector fields has only quadratic-linear relations and posesses a Poincaré-Birkhoff-Witt basis. We use the concept of universal (higher order) differential calculus associated with a given left-covariant first order differential calculus. It turns out that the space of left-invariant k-forms has the dimension $N^{2} - 1\choose k$ as in the case of the corresponding classical Lie group SL(N).
Źródło:
Banach Center Publications; 1997, 40, 1; 185-191
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Connections in regular Poisson manifolds over ℝ-Lie foliations
Autorzy:
Kubarski, Jan
Powiązania:
https://bibliotekanauki.pl/articles/1207678.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Lie algebroid
ℝ-Lie foliation
Poisson manifold
closed transversal
flat connection with singularites along closed transversals
Opis:
The subject of this paper is the notion of the connection in a regular Poisson manifold M, defined as a splitting of the Atiyah sequence of its Lie algebroid. In the case when the characteristic foliation F is an ℝ-Lie foliation, the fibre integral operator along the adjoint bundle is used to define the Euler class of the Poisson manifold M. When M is oriented 3-dimensional, the notion of the index of a local flat connection with singularities along a closed transversal is defined. If, additionally, F has compact leaves (then F is a fibration over $S^{1}$), an analogue of the Euler-Poincaré-Hopf index theorem for flat connections with singularities along closed transversals is obtained.
Źródło:
Banach Center Publications; 2000, 51, 1; 141-149
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The continuity of Lie homomorphisms
Autorzy:
Aupetit, Bernard
Mathieu, Martin
Powiązania:
https://bibliotekanauki.pl/articles/1206145.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Lie homomorphisms
Banach algebras
spectrally bounded maps
Opis:
We prove that the separating space of a Lie homomorphism from a Banach algebra onto a Banach algebra is contained in the centre modulo the radical.
Źródło:
Studia Mathematica; 2000, 138, 2; 193-199
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the joint spectral radius of a nilpotent Lie algebra of matrices
Autorzy:
Boasso, Enrico
Powiązania:
https://bibliotekanauki.pl/articles/1217349.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Taylor spectrum
joint spectral radius
nilpotent Lie algebras
Opis:
For a complex nilpotent finite-dimensional Lie algebra of matrices, and a Jordan-Hölder basis of it, we prove a spectral radius formula which extends a well-known result for commuting matrices.
Źródło:
Studia Mathematica; 1999, 132, 1; 15-27
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The upper bound of the number of eigenvalues for a class of perturbed Dirichlet forms
Autorzy:
Cupała, Wiesław
Powiązania:
https://bibliotekanauki.pl/articles/1289649.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
eigenvalue asymptotics
Dirichlet form
Markov process
Lie group
Opis:
The theory of Markov processes and the analysis on Lie groups are used to study the eigenvalue asymptotics of Dirichlet forms perturbed by scalar potentials.
Źródło:
Studia Mathematica; 1995, 113, 2; 109-125
0039-3223
Pojawia się w:
Studia Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Continuous linear extension operators on spaces of holomorphic functions on closed subgroups of a complex Lie group
Autorzy:
Thai, Do
Hoang, Dinh
Powiązania:
https://bibliotekanauki.pl/articles/1294150.pdf
Data publikacji:
1999
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
complex Lie group
linear topological invariant
right inverse
Opis:
We show that the restriction operator of the space of holomorphic functions on a complex Lie group to an analytic subset V has a continuous linear right inverse if it is surjective and if V is a finite branched cover over a connected closed subgroup Γ of G. Moreover, we show that if Γ and G are complex Lie groups and V ⊂ Γ × G is an analytic set such that the canonical projection $π_1 : V → Γ$ is finite and proper, then $R_V : O(Γ × G) → Im R_V ⊂ O(V)$ has a right inverse
Źródło:
Annales Polonici Mathematici; 1999, 71, 2; 105
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The BV-algebra of a Jacobi manifold
Autorzy:
Vaisman, Izu
Powiązania:
https://bibliotekanauki.pl/articles/1208014.pdf
Data publikacji:
2000
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Jacobi manifolds
BV-algebras
Lie bialgebroids
Gerstenhaber algebras
Opis:
We show that the Gerstenhaber algebra of the 1-jet Lie algebroid of a Jacobi manifold has a canonical exact generator, and discuss duality between its homology and the Lie algebroid cohomology. We also give new examples of Lie bialgebroids over Poisson manifolds.
Źródło:
Annales Polonici Mathematici; 2000, 73, 3; 275-290
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Controllability of right invariant systems on semi-simple Lie groups
Autorzy:
El Assoudi, R.
Gauthier, J.
Kupka, I.
Powiązania:
https://bibliotekanauki.pl/articles/1359667.pdf
Data publikacji:
1995
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
invariant vector fields
controllability
root systems
semi-simple Lie algebras
Opis:
We deal with controllability of right invariant control systems on semi-simple Lie groups. We recall the history of the problem and the successive results. We state the final complete result, with a sketch of proof.
Źródło:
Banach Center Publications; 1995, 32, 1; 199-208
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Continuous transformation groups on spaces
Autorzy:
Spallek, K.
Powiązania:
https://bibliotekanauki.pl/articles/1312663.pdf
Data publikacji:
1991
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
differentiable spaces
differentiable groups
Lie groups
transformation groups
formal groups
Opis:
A differentiable group is a group in the category of (reduced and nonreduced) differentiable spaces. Special cases are the rationals ℚ, Lie groups, formal groups over ℝ or ℂ; in general there is some mixture of those types, the general structure, however, is not yet completely determined. The following gives as a corollary a first essential answer. It is shown, more generally,that a locally compact topological transformation group, operating effectively on a differentiable space X (which satisfies some mild geometric property) is in fact a Lie group and operates differentiably on X. Special cases have already been known: X a manifold (Montgomery-Zippin), X a reduced (Kerner) or nonreduced (W. Kaup) complex space. The proof requires some analysis on arbitrary differentiable spaces. There one has for example in general no finitely generated ideals as in the case of complex spaces. As a corollary one obtains: The reduction of a locally compact differentiable group is a Lie group (by different methods also proved by Pasternak-Winiarski). It was already proved before that any differentiable group can be uniquely extended to a smallest locally compact differentiable group (as a dense subgroup). The study of the nonreduced parts of differentiable groups remains to be completed.
Źródło:
Annales Polonici Mathematici; 1991, 55, 1; 301-320
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Lie algebras of vector fields related to Riemannian foliations
Autorzy:
Rybicki, Tomasz
Powiązania:
https://bibliotekanauki.pl/articles/1311816.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Riemannian foliation
Lie algebra
ideal
isomorphism
vector field
generalized manifold
stratification
Opis:
Riemannian foliations constitute an important type of foliated structures. In this note we prove two theorems connecting the algebraic structure of Lie algebras of foliated vector fields with the smooth structure of a Riemannian foliation.
Źródło:
Annales Polonici Mathematici; 1993, 58, 2; 111-122
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Some division theorems for vector fields
Autorzy:
Zajtz, Andrzej
Powiązania:
https://bibliotekanauki.pl/articles/1311886.pdf
Data publikacji:
1993
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
Lie bracket of vector fields
bounds to flow and its prolongations
Opis:
This paper is concerned with the problem of divisibility of vector fields with respect to the Lie bracket [X,Y]. We deal with the local divisibility. The methods used are based on various estimates, in particular those concerning prolongations of dynamical systems. A generalization to polynomials of the adjoint operator (X) is given.
Źródło:
Annales Polonici Mathematici; 1993, 58, 1; 19-28
0066-2216
Pojawia się w:
Annales Polonici Mathematici
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On Lie algebras in braided categories
Autorzy:
Pareigis, Bodo
Powiązania:
https://bibliotekanauki.pl/articles/1342720.pdf
Data publikacji:
1997
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
braided category
universal enveloping algebra
braided Hopf algebra
graded Lie algebra
Opis:
The category of group-graded modules over an abelian group $G$ is a monoidal category. For any bicharacter of $G$ this category becomes a braided monoidal category. We define the notion of a Lie algebra in this category generalizing the concepts of Lie super and Lie color algebras. Our Lie algebras have $n$-ary multiplications between various graded components. They possess universal enveloping algebras that are Hopf algebras in the given category. Their biproducts with the group ring are noncommutative noncocommutative Hopf algebras some of them known in the literature. Conversely the primitive elements of a Hopf algebra in the category form a Lie algebra in the above sense.
Źródło:
Banach Center Publications; 1997, 40, 1; 139-158
0137-6934
Pojawia się w:
Banach Center Publications
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Topological realization of a family of pseudoreflection groups
Autorzy:
Notbohm, Dietrich
Powiązania:
https://bibliotekanauki.pl/articles/1205400.pdf
Data publikacji:
1998
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
pseudoreflection groups
p-compact group
classifying spaces
compact Lie group
polynomial algebra
Opis:
We are interested in a topological realization of a family of pseudoreflection groups $G ⊂ GL(n,{\sym F}_p )$; i.e. we are looking for topological spaces whose mod-p cohomology is isomorphic to the ring of invariants ${\sym F}_p [x_1,..., x_n]^G$. Spaces of this type give partial answers to a problem of Steenrod, namely which polynomial algebras over ${\sym F}_p $ can appear as the mod-p cohomology of a space. The family under consideration is given by pseudoreflection groups which are subgroups of the wreath product $ℤ/q ≀Σ_n$ where q divides p - 1 and where p is odd. Let G be such a subgroup acting on the polynomial algebra $A:= {\sym F}_p [x_1,..., x_n]$. We show that there exists a space X such that $H*(X;{\sym F}_p )≅ A^G$ which is again a polynomial algebra. Examples of polynomial algebras of this form are given by the mod-p cohomology of the classifying spaces of special orthogonal groups or of symplectic groups.
 The construction uses products of classifying spaces of unitary groups as building blocks which are glued together via information encoded in a full subcategory of the orbit category of the group G. Using this construction we also show that the homotopy type of the p-adic completion of these spaces is completely determined by the mod-p cohomology considered as an algebra over the Steenrod algebra. Moreover, we calculate the set of homotopy classes of self maps of the completed spaces.
Źródło:
Fundamenta Mathematicae; 1998, 155, 1; 1-31
0016-2736
Pojawia się w:
Fundamenta Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 19

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