TY - JOUR
T1 - On blocks of defect two and one simple module, and Lie algebra structure of HHⁱ
AU - Benson, David
AU - Kessar, Radha
AU - Linckelmann, Markus
N1 - The first author thanks City, University of London for its hospitality during the preparation of this paper.
PY - 2017/12
Y1 - 2017/12
N2 - Let k be a field of odd prime characteristic p. We calculate the Lie algebra structure of the first Hochschild cohomology of a class of quantum complete intersections over k. As a consequence, we prove that if B is a defect 2-block of a finite group algebra kG whose Brauer correspondent C has a unique isomorphism class of simple modules, then a basic algebra of B is a local algebra which can be generated by at most 2√ I elements, where I is the inertial index of B, and where we assume that k is a splitting field for B and C.
AB - Let k be a field of odd prime characteristic p. We calculate the Lie algebra structure of the first Hochschild cohomology of a class of quantum complete intersections over k. As a consequence, we prove that if B is a defect 2-block of a finite group algebra kG whose Brauer correspondent C has a unique isomorphism class of simple modules, then a basic algebra of B is a local algebra which can be generated by at most 2√ I elements, where I is the inertial index of B, and where we assume that k is a splitting field for B and C.
U2 - 10.1016/j.jpaa.2017.02.010
DO - 10.1016/j.jpaa.2017.02.010
M3 - Article
VL - 221
SP - 2953
EP - 2973
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
IS - 12
ER -