TY - JOUR

T1 - The Anick Complex and the Hochschild Cohomology of the Manturov (2,3)-Group

AU - AlHussein, H.

AU - Kolesnikov, P. S.

PY - 2020/1

Y1 - 2020/1

N2 - The Manturov (2, 3)-group G32 is the group generated by three elements a, b, and c with defining relations a(2) = b(2) = c(2) = (abc)(2) = 1. We explicitly calculate the Anick chain complex for G32 by algebraic discrete Morse theory and evaluate the Hochschild cohomology groups of the group algebra kG32 with coefficients in all 1-dimensional bimodules over a field kof characteristic zero.

AB - The Manturov (2, 3)-group G32 is the group generated by three elements a, b, and c with defining relations a(2) = b(2) = c(2) = (abc)(2) = 1. We explicitly calculate the Anick chain complex for G32 by algebraic discrete Morse theory and evaluate the Hochschild cohomology groups of the group algebra kG32 with coefficients in all 1-dimensional bimodules over a field kof characteristic zero.

KW - Hochschild cohomology

KW - Anick resolution

KW - Grobner-Shirshov basis

KW - Morse matching

KW - MORSE-THEORY

KW - BASES

U2 - 10.1134/S0037446620010024

DO - 10.1134/S0037446620010024

M3 - Article

VL - 61

SP - 11

EP - 20

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 1

ER -