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

Standard

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

In: Journal of Algebra and its Applications, Vol. 20, No. 8, 2150134, 08.2021.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{41c87f92778647d3ad47b96174de447d,

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

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.",

keywords = "Anick resolution, Gr{\"o}bner-Shirshov basis, Hochschild cohomology, Morse matching",

author = "Hassan Alhussein",

year = "2021",

month = aug,

doi = "10.1142/S0219498821501346",

language = "English",

volume = "20",

journal = "Journal of Algebra and its Applications",

issn = "0219-4988",

publisher = "World Scientific Publishing Co. Pte Ltd",

number = "8",

}

RIS

TY - JOUR

T1 - Anick complex, Hochschild cohomology, Hilbert and Poincare series of the Manturov (3,4)-group

AU - Alhussein, Hassan

PY - 2021/8

Y1 - 2021/8

N2 - 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.

AB - 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.

KW - Anick resolution

KW - Gröbner-Shirshov basis

KW - Hochschild cohomology

KW - Morse matching

UR - http://www.scopus.com/inward/record.url?scp=85089140978&partnerID=8YFLogxK

U2 - 10.1142/S0219498821501346

DO - 10.1142/S0219498821501346

M3 - Article

AN - SCOPUS:85089140978

VL - 20

JO - Journal of Algebra and its Applications

JF - Journal of Algebra and its Applications

SN - 0219-4988

IS - 8

M1 - 2150134

ER -

ID: 24986008