Anick complex, Hochschild cohomology, Hilbert and Poincare series of the Manturov (3,4)-group

Hassan Alhussein

Research output: Contribution to journalArticlepeer-review

Abstract

The Manturov (3, 4)-group G43 is the group generated by four elements a, b, c, d with defining relations a2 = b2 = c2 = d2 = (abcd)2 = (acdb)2 = (adbc)2 = 1. We apply the algebraic discrete Morse theory to calculate the Anick chain complex for G43, evaluate the Hochschild cohomology groups of the group algebra G43 with coefficients in all 1-dimensional bimodules over a field of characteristic zero, and derive its Hilbert and Poincare series.

Original languageEnglish
Article number2150134-1
JournalJournal of Algebra and its Applications
DOIs
Publication statusPublished - 24 Jul 2020

Keywords

  • Anick resolution
  • Gröbner-Shirshov basis
  • Hochschild cohomology
  • Morse matching

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