The first Hochschild cohomology group of quantum matrices and the quantum special linear group
نویسندگان
چکیده
منابع مشابه
Hochschild cohomology group of quantum matrices and the quantum special linear group
We calculate the first Hochschild cohomology group of quantum matrices, the quantum general linear group and the quantum special linear group in the generic case when the deformation parameter is not a root of unity. As a corollary, we obtain information about twisted Hochschild homology of these algebras. 2000 Mathematics subject classification: 16E40, 16W35, 17B37, 17B40, 20G42
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...
متن کاملGerstenhaber 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 Cohomology and Quantum Drinfeld Hecke Algebras
Abstract. Quantum Drinfeld Hecke algebras are generalizations of Drinfeld Hecke algebras in which polynomial rings are replaced by quantum polynomial rings. We identify these algebras as deformations of skew group algebras, giving an explicit connection to Hochschild cohomology. We compute the relevant part of Hochschild cohomology for actions of many reflection groups and we exploit computatio...
متن کاملQuantum random walks and vanishing of the second Hochschild cohomology
Given a conditionally completely positive map L on a unital ∗-algebra A, we find an interesting connection between the second Hochschild cohomology of A with coefficients in the bimodule EL = Ba(A⊕M) of adjointable maps, where M is the GNS bimodule of L, and the possibility of constructing a quantum random walk (in the sense of [2, 11, 13, 16]) corresponding to L.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Noncommutative Geometry
سال: 2007
ISSN: 1661-6952
DOI: 10.4171/jncg/8