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The Batalin-Vilkovisky Algebra on Hochschild Cohomology Induced by Infinity Inner Products

Thomas Tradler (2008)

Annales de l’institut Fourier

We define a BV-structure on the Hochschild cohomology of a unital, associative algebra $A$ with a symmetric, invariant and non-degenerate inner product. The induced Gerstenhaber algebra is the one described in Gerstenhaber’s original paper on Hochschild-cohomology. We also prove the corresponding theorem in the homotopy case, namely we define the BV-structure on the Hochschild-cohomology of a unital $A_{\infty}$ -algebra with a symmetric and non-degenerate $\infty$ -inner product.

The bicrossed products of $H_{4}$ and $H_{8}$

Daowei Lu, Yan Ning, Dingguo Wang (2020)

Czechoslovak Mathematical Journal

Let $H_{4}$ and $H_{8}$ be the Sweedler’s and Kac-Paljutkin Hopf algebras, respectively. We prove that any Hopf algebra which factorizes through $H_{8}$ and $H_{4}$ (equivalently, any bicrossed product between the Hopf algebras $H_{8}$ and $H_{4}$ ) must be isomorphic to one of the following four Hopf algebras: $H_{8} \otimes H_{4}, H_{32, 1}, H_{32, 2}, H_{32, 3}$ . The set of all matched pairs $(H_{8}, H_{4}, ▹, ◃)$ is explicitly described, and then the associated bicrossed product is given by generators and relations.

The Boolean algebra and central Galois algebras.

Szeto, George, Xue, Lianyong (2001)

International Journal of Mathematics and Mathematical Sciences

The Boolean algebra of Galois algebras.

Szeto, George, Xue, Lianyong (2003)

International Journal of Mathematics and Mathematical Sciences

The Brauer and Brauer-Taylor groups of a symmetric monoidal category

Enrico M. Vitale (1996)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

The Brauer ring of a commutative ring

Chen, Chengxiang (1993)

Portugaliae mathematica

The canonical algebras

Claus Michael Ringel (1990)

Banach Center Publications

The category of abelian Hopf algebras

Andrzej Skowroński (1980)

Fundamenta Mathematicae

The category of groupoid graded modules

Patrik Lundström (2004)

Colloquium Mathematicae

We introduce the abelian category R-gr of groupoid graded modules and give an answer to the following general question: If U: R-gr → R-mod denotes the functor which associates to any graded left R-module M the underlying ungraded structure U(M), when does either of the following two implications hold: (I) M has property X ⇒ U(M) has property X; (II) U(M) has property X ⇒ M has property X? We treat the cases when X is one of the properties: direct summand, free, finitely generated, finitely presented,...

The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences.

Claus Michael Ringel (1991)

Mathematische Zeitschrift

The category of partial Doi-Hopf modules and functors

Q.-G. Chen, D.-G. Wang (2013)

Rendiconti del Seminario Matematico della Università di Padova

The catenarity of the positive part of the quantized enveloping algebra of a simple Lie algebra of type $B_{2}$ . (La caténarité de la partie positive de l'algèbre enveloppante quantifiée de l'algèbre de Lie simple de type $B_{2}$ .)

Malliavin, Marie Paule (1994)

Beiträge zur Algebra und Geometrie

The center of the Dipper Donkin quantized matrix algebra.

Jakobsen, Hans Plesner, Zhang, Hechun (1997)

Beiträge zur Algebra und Geometrie

The centre of completed group algebras of pro- $p$ groups.

Ardakov, Konstantin (2004)

Documenta Mathematica

The characteristic variety of a generic foliation

Jorge Vitório Pereira (2012)

Journal of the European Mathematical Society

We confirm a conjecture of Bernstein–Lunts which predicts that the characteristic variety of a generic polynomial vector field has no homogeneous involutive subvarieties besides the zero section and subvarieties of fibers over singular points.