منابع مشابه
Group Actions on Algebras and the Graded Lie Structure of Hochschild Cohomology
Hochschild cohomology governs deformations of algebras, and its graded Lie structure plays a vital role. We study this structure for the Hochschild cohomology of the skew group algebra formed by a finite group acting on an algebra by automorphisms. We examine the Gerstenhaber bracket with a view toward deformations and developing bracket formulas. We then focus on the linear group actions and p...
متن کاملSelf-injective Algebras and the Second Hochschild Cohomology Group
In this paper we study the second Hochschild cohomology group HH(Λ) of a finite dimensional algebra Λ. In particular, we determine HH(Λ) where Λ is a finite dimensional self-injective algebra of finite representation type over an algebraically closed field K and show that this group is zero for most such Λ; we give a basis for HH(Λ) in the few cases where it is not zero.
متن کاملHigher order Hochschild cohomology
Following ideas of Pirashvili, we define higher order Hochschild cohomology over spheres S defined for any commutative algebra A and module M . When M = A, we prove that this cohomology is equipped with graded commutative algebra and degree d Lie algebra structures as well as with Adams operations. All operations are compatible in a suitable sense. These structures are related to Brane topology...
متن کاملAlternated Hochschild Cohomology
In this paper we construct a graded Lie algebra on the space of cochains on a Z2-graded vector space that are skew-symmetric in the odd variables. The Lie bracket is obtained from the classical Gerstenhaber bracket by (partial) skew-symmetrization; the coboundary operator is a skew-symmetrized version of the Hochschild differential. We show that an order-one element m satisfying the zero-square...
متن کاملHochschild Cohomology of Group Extensions of Quantum Symmetric Algebras
Abstract. Quantum symmetric algebras (or noncommutative polynomial rings) arise in many places in mathematics. In this article we find the multiplicative structure of their Hochschild cohomology when the coefficients are in an arbitrary bimodule algebra. When this bimodule algebra is a finite group extension (under a diagonal action) of a quantum symmetric algebra, we give explicitly the graded...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2020
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-020-02557-x