Hochschild Cohomology of Group Extensions of Quantum Symmetric Algebras
نویسندگان
چکیده
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 vector space structure. This yields a complete description of the Hochschild cohomology ring of the corresponding skew group algebra.
منابع مشابه
Gerstenhaber Brackets on Hochschild Cohomology of Quantum Symmetric Algebras and Their Group Extensions
We construct chain maps between the bar and Koszul resolutions for a quantum symmetric algebra (skew polynomial ring). This construction uses a recursive technique involving explicit formulae for contracting homotopies. We use these chain maps to compute the Gerstenhaber bracket, obtaining a quantum version of the Schouten-Nijenhuis bracket on a symmetric algebra (polynomial ring). We compute b...
متن کاملHochschild Homology and Split Pairs
We study the Hochschild homology of algebras related via split pairs, and apply this to fibre products, trivial extensions, monomial algebras, graded-commutative algebras and quantum complete intersections. In particular, we compute lower bounds for the dimensions of both the Hochschild homology and cohomology groups of quantum complete intersections.
متن کاملResearch Program
I work on the cohomology, structure, and representations of various types of rings, such as Hopf algebras and group-graded algebras. My research program involves collaborations with many mathematicians, including work with postdocs and graduate students. Below is a summary of some of my past and ongoing research projects, which fall loosely into three categories: Hochschild cohomology and defor...
متن کاملPast Research
I work on the cohomology, structure, and representations of various types of rings, such as Hopf algebras and group-graded algebras. My research program has involved collaborations with many mathematicians, including work with postdocs and graduate students. Below is a summary of some of my past research projects, which fall loosely into three categories: Hochschild cohomology and deformations....
متن کامل