Some results on the Hochschild cohomology of group algebras

AbstractWe give an explicit approach for Bockstein homomorphisms of the Hochschild cohomology of a group algebra and of a block algebra of a finite group and we show some properties. To give explicit definitions for these maps we use an additive decomposition and a product formula for the Hochschild cohomology of group algebras given by Siegel and Witherspoon in 1999. For an algebraically closed field

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Complex group algebras of the direct product of non-isomorphic Suzuki groups

Journal of Algebra and Its Applications ◽

10.1142/s021949882050036x ◽

2019 ◽

Vol 19 (02) ◽

pp. 2050036

Author(s):

Morteza Baniasad Azad ◽

Behrooz Khosravi

Keyword(s):

Direct Product ◽

Group Algebra ◽

Irreducible Character ◽

Prime Numbers ◽

Product Formula ◽

Character Degrees ◽

Group Algebras ◽

Complex Group ◽

Complex Group Algebra ◽

Suzuki Groups

In this paper, we prove that the direct product [Formula: see text], where [Formula: see text] are distinct numbers, is uniquely determined by its complex group algebra. Particularly, we show that the direct product [Formula: see text], where [Formula: see text]’s are distinct odd prime numbers, is uniquely determined by its order and three irreducible character degrees.

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EXAMPLES OF FINITE-DIMENSIONAL POINTED HOPF ALGEBRAS IN CHARACTERISTIC 2

Glasgow Mathematical Journal ◽

10.1017/s0017089520000579 ◽

2020 ◽

pp. 1-14

Author(s):

NICOLÁS ANDRUSKIEWITSCH ◽

DIRCEU BAGIO ◽

SARADIA DELLA FLORA ◽

DAIANA FLÔRES

Keyword(s):

Hopf Algebras ◽

Abelian Groups ◽

Vector Spaces ◽

Group Algebras ◽

Finite Abelian Groups ◽

Finite Dimensional ◽

Pointed Hopf Algebras ◽

Characteristic 2 ◽

Nichols Algebras ◽

Kirillov Dimension

Abstract We present new examples of finite-dimensional Nichols algebras over fields of characteristic 2 from braided vector spaces that are not of diagonal type, admit realizations as Yetter–Drinfeld modules over finite abelian groups, and are analogous to Nichols algebras of finite Gelfand–Kirillov dimension in characteristic 0. New finite-dimensional pointed Hopf algebras over fields of characteristic 2 are obtained by bosonization with group algebras of suitable finite abelian groups.

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The Gerstenhaber structure on the Hochschild cohomology of a class of special biserial algebras

Journal of Algebra ◽

10.1016/j.jalgebra.2021.03.032 ◽

2021 ◽

Vol 580 ◽

pp. 264-298

Author(s):

Joanna Meinel ◽

Van C. Nguyen ◽

Bregje Pauwels ◽

María Julia Redondo ◽

Andrea Solotar

Keyword(s):

Hochschild Cohomology ◽

Special Biserial Algebras

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Dominant and global dimension of blocks of quantised Schur algebras

Mathematische Zeitschrift ◽

10.1007/s00209-021-02792-w ◽

2021 ◽

Author(s):

Ming Fang ◽

Wei Hu ◽

Steffen Koenig

Keyword(s):

Hecke Algebras ◽

Symmetric Groups ◽

Global Dimension ◽

Group Algebras ◽

Dominant Dimension ◽

Schur Algebras ◽

Homological Dimensions ◽

Weyl Duality

AbstractGroup algebras of symmetric groups and their Hecke algebras are in Schur-Weyl duality with classical and quantised Schur algebras, respectively. Two homological dimensions, the dominant dimension and the global dimension, of the indecomposable summands (blocks) of these Schur algebras S(n, r) and $$S_q(n,r)$$ S q ( n , r ) with $$n \geqslant r$$ n ⩾ r are determined explicitly, using a result on derived invariance in Fang, Hu and Koenig (J Reine Angew Math 770:59–85, 2021).

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