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    Wyświetlanie 1-10 z 10
    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:
    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:
    Weak products of universal algebras
    Autorzy:
    Sain, Ildikó
    Powiązania:
    https://bibliotekanauki.pl/articles/1361096.pdf
    Data publikacji:
    1993
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    universal algebra
    algebraic logic
    cylindric algebras
    Opis:
    Weak direct products of arbitrary universal algebras are introduced. The usual notion for groups and rings is a special case. Some universal algebraic properties are proved and applications to cylindric and polyadic algebras are considered.
    Źródło:
    Banach Center Publications; 1993, 28, 1; 311-318
    0137-6934
    Pojawia się w:
    Banach Center Publications
    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:
    Reduction of differential equations
    Autorzy:
    Skórnik, Krystyna
    Wloka, Joseph
    Powiązania:
    https://bibliotekanauki.pl/articles/1207630.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    differential algebra
    linear differential equations
    operational calculus
    Opis:
    Let (F,D) be a differential field with the subfield of constants C (c ∈ C iff Dc=0). We consider linear differential equations (1) $Ly = D^{n}y + a_{n-1}D^{n-1}y+...+ a_{0}y = 0$, where $a_0,... ,a_n ∈ F$, and the solution y is in F or in some extension E of F (E ⊇ F). There always exists a (minimal, unique) extension E of F, where Ly=0 has a full system $y_1,... ,y_n$ of linearly independent (over C) solutions; it is called the Picard-Vessiot extension of F E = PV(F,Ly=0). The Galois group G(E|F) of an extension field E ⊇ F consists of all differential automorphisms of E leaving the elements of F fixed. If E = PV(F,Ly=0) is a Picard-Vessiot extension, then the elements g ∈ G(E|F) are n × n matrices, n= ord L, with entries from C, the field of constants. Is it possible to solve an equation (1) by means of linear differential equations of lower order ≤ n-1? We answer this question by giving neccessary and sufficient conditions concerning the Galois group G(E|F) and its Lie algebra A(E|F).
    Źródło:
    Banach Center Publications; 2000, 53, 1; 199-204
    0137-6934
    Pojawia się w:
    Banach Center Publications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    $L^p$-spaces and quantum dynamical semigroups
    Autorzy:
    Goldstein, Stanisław
    Lindsay, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/1342202.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    C*-algebra
    symmetric embedding
    von Neumann algebra
    weight
    $L^p$-space
    Markov semigroup
    positivity
    KMS-symmetry
    Dirichlet form
    Źródło:
    Banach Center Publications; 1998, 43, 1; 211-216
    0137-6934
    Pojawia się w:
    Banach Center Publications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Dilation theorems for completely positive maps and map-valued measures
    Autorzy:
    Hensz-Chądzyńska, Ewa
    Jajte, Ryszard
    Paszkiewicz, Adam
    Powiązania:
    https://bibliotekanauki.pl/articles/1342207.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    completely positive map
    von Neumann algebra
    dilation
    map-valued measure
    Opis:
    The Stinespring theorem is reformulated in terms of conditional expectations in a von Neumann algebra. A generalisation for map-valued measures is obtained.
    Źródło:
    Banach Center Publications; 1998, 43, 1; 231-239
    0137-6934
    Pojawia się w:
    Banach Center Publications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Non-Leibniz algebras with logarithms do not have the trigonometric identity
    Autorzy:
    Przeworska-Rolewicz, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/1207627.pdf
    Data publikacji:
    2000
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    sine mapping
    algebra with unit
    algebraic analysis
    logarithmic mapping
    Leibniz condition
    cosine mapping
    Opis:
    Let X be a Leibniz algebra with unit e, i.e. an algebra with a right invertible linear operator D satisfying the Leibniz condition: D(xy) = xDy + (Dx)y for x,y belonging to the domain of D. If logarithmic mappings exist in X, then cosine and sine elements C(x) and S(x) defined by means of antilogarithmic mappings satisfy the Trigonometric Identity, i.e. $[C(x)]^2 + [S(x)]^2 = e$ whenever x belongs to the domain of these mappings. The following question arises: Do there exist non-Leibniz algebras with logarithms such that the Trigonometric Identity is satisfied? We shall show that in non-Leibniz algebras with logarithms the Trigonometric Identity does not exist. This means that the above question has a negative answer, i.e. the Leibniz condition in algebras with logarithms is a necessary and sufficient condition for the Trigonometric Identity to hold.
    Źródło:
    Banach Center Publications; 2000, 53, 1; 177-189
    0137-6934
    Pojawia się w:
    Banach Center Publications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The cohomology algebras of orientable Seifert manifolds and applications to Lusternik-Schnirelmann category
    Autorzy:
    Bryden, J.
    Zvengrowski, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/1341772.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Matematyczny PAN
    Tematy:
    cup products
    cup product length
    Lusternik-Schnirelmann category
    degree one maps
    diagonal map
    Seifert manifolds
    cohomology algebra
    Opis:
    This note gives a complete description of the cohomology algebra of any orientable Seifert manifold with ℤ/p coefficients, for an arbitrary prime p. As an application, the existence of a degree one map from an orientable Seifert manifold onto a lens space is completely determined. A second application shows that the Lusternik-Schnirelmann category for a large class of Seifert manifolds is equal to 3, which in turn is used to verify the Ganea conjecture for these Seifert manifolds.
    Źródło:
    Banach Center Publications; 1998, 45, 1; 25-39
    0137-6934
    Pojawia się w:
    Banach Center Publications
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-10 z 10

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