Hochschild cohomology of algebras of dihedral type, I: The family $D(3\mathcal K)$ in characteristic $2$

DOI10.1090/S1061-0022-05-00886-1zbMath1087.16007OpenAlexW1504467367MaRDI QIDQ3376464

A. I. Generalov

Publication date: 23 March 2006

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s1061-0022-05-00886-1

zbMATH Keywords

relationsgeneratorsprincipal blocksHochschild cohomology algebrasalgebras of dihedral typedihedral defect groups

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Modular representations and characters (20C20) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Representations of quivers and partially ordered sets (16G20) Representations of finite groups of Lie type (20C33)

Related Items

Hochschild cohomology for algebras of semidihedral type. X: Cohomology algebra for the exceptional local algebras ⋮ Hochschild cohomology of algebras of quaternion type. IV: Cohomology algebra for exceptional local algebras ⋮ Cohomology of algebras of dihedral type. V ⋮ Hochschild cohomology for algebras of dihedral type. IV: The family \(D(2\mathcal B)(k,s,0)\). ⋮ Hochschild cohomology for algebras of dihedral type. V. the family \(D(3\mathcal{K})\) in characteristic different from 2 ⋮ Hochschild cohomology for algebras of dihedral type. VII: The family \(D(3\mathcal{R})\) ⋮ Hochschild cohomology of algebras of dihedral type. VIII: Hochshild cohomology algebra for the family \(D(2\mathcal{B})(k, s, 0)\) in characteristic 2 ⋮ Hochschild comohology for algebras of dihedral type, VI. The family $D(2\mathcal B)(k,s,1)$

Cites Work

• Unnamed Item
• Unnamed Item
• Cohomology of algebras of semidihedral type. III: The family \(SD(3\mathcal K)\).
• Blocks of tame representation type and related algebras
• Derived equivalence classification of algebras of dihedral, semidihedral, and quaternion type
• A derived equivalence for blocks with dihedral defect groups
• The alternating syzygy behavior of monomial algebras
• Hochschild cohomology algebra of abelian groups
• Cohomology of algebras of semidihedral type. II.
• Cohomology of algebras of dihedral type. IV: The family \(D(2{\mathcal B})\).
• Cohomology of algebras of dihedral type. III: The family \(D(2{\mathcal A})\).
• Twisted bimodules and Hochschild cohomology for self-injective algebras of class \(A_n\). II.
• The even Hochschild cohomology ring of a block with cyclic defect group
• The cohomology structure of an associative ring
• Cohomology theory in abstract groups. I
• Algebras and Dihedral Defect Groups
• Principal blocks of groups with dihedral sylow 2-subgroups
• Twisted bimodules and Hochschild cohomology for self-injective algebras of class An
• The Hochschild Cohomology Ring of a Group Algebra
• Derived Equivalences As Derived Functors
• The hochschild cohomology ring of a modular group algebra: the commutative case