GERSTENHABER BRACKET ON THE HOCHSCHILD COHOMOLOGY VIA AN ARBITRARY RESOLUTION

Standard

GERSTENHABER BRACKET ON THE HOCHSCHILD COHOMOLOGY VIA AN ARBITRARY RESOLUTION. / Volkov, Yury .

In: Proceedings of the Edinburgh Mathematical Society, Vol. 62, No. 3, 01.08.2019, p. 817-836.

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

Author

Volkov, Yury . / GERSTENHABER BRACKET ON THE HOCHSCHILD COHOMOLOGY VIA AN ARBITRARY RESOLUTION. In: Proceedings of the Edinburgh Mathematical Society. 2019 ; Vol. 62, No. 3. pp. 817-836.

BibTeX

@article{6e671e8bf37e479fbf58729989d6ca13,

title = "GERSTENHABER BRACKET ON THE HOCHSCHILD COHOMOLOGY VIA AN ARBITRARY RESOLUTION",

abstract = "We prove formulas of different types that allow us to calculate the Gerstenhaber bracket on the Hochschild cohomology of an algebra using some arbitrary projective bimodule resolution for it. Using one of these formulas, we give a new short proof of the derived invariance of the Gerstenhaber algebra structure on Hochschild cohomology. We also give some new formulas for the Connes differential on the Hochschild homology that lead to formulas for the Batalin-Vilkovisky (BV) differential on the Hochschild cohomology in the case of symmetric algebras. Finally, we use one of the obtained formulas to provide a full description of the BV structure and, correspondingly, the Gerstenhaber algebra structure on the Hochschild cohomology of a class of symmetric algebras.",

keywords = "Hochschild cohomology, Gerstenhaber bracket, bimodule resolution, derived equivalence, BATALIN-VILKOVISKY ALGEBRA, COMPARISON MORPHISMS, RING",

author = "Yury Volkov",

year = "2019",

month = aug,

day = "1",

doi = "10.1017/S0013091518000901",

language = "Английский",

volume = "62",

pages = "817--836",

journal = "Proceedings of the Edinburgh Mathematical Society",

issn = "0013-0915",

publisher = "Cambridge University Press",

number = "3",

}

RIS

TY - JOUR

T1 - GERSTENHABER BRACKET ON THE HOCHSCHILD COHOMOLOGY VIA AN ARBITRARY RESOLUTION

AU - Volkov, Yury

PY - 2019/8/1

Y1 - 2019/8/1

N2 - We prove formulas of different types that allow us to calculate the Gerstenhaber bracket on the Hochschild cohomology of an algebra using some arbitrary projective bimodule resolution for it. Using one of these formulas, we give a new short proof of the derived invariance of the Gerstenhaber algebra structure on Hochschild cohomology. We also give some new formulas for the Connes differential on the Hochschild homology that lead to formulas for the Batalin-Vilkovisky (BV) differential on the Hochschild cohomology in the case of symmetric algebras. Finally, we use one of the obtained formulas to provide a full description of the BV structure and, correspondingly, the Gerstenhaber algebra structure on the Hochschild cohomology of a class of symmetric algebras.

AB - We prove formulas of different types that allow us to calculate the Gerstenhaber bracket on the Hochschild cohomology of an algebra using some arbitrary projective bimodule resolution for it. Using one of these formulas, we give a new short proof of the derived invariance of the Gerstenhaber algebra structure on Hochschild cohomology. We also give some new formulas for the Connes differential on the Hochschild homology that lead to formulas for the Batalin-Vilkovisky (BV) differential on the Hochschild cohomology in the case of symmetric algebras. Finally, we use one of the obtained formulas to provide a full description of the BV structure and, correspondingly, the Gerstenhaber algebra structure on the Hochschild cohomology of a class of symmetric algebras.

KW - Hochschild cohomology

KW - Gerstenhaber bracket

KW - bimodule resolution

KW - derived equivalence

KW - BATALIN-VILKOVISKY ALGEBRA

KW - COMPARISON MORPHISMS

KW - RING

UR - http://www.scopus.com/inward/record.url?scp=85061278358&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/gerstenhaber-bracket-hochschild-cohomology-via-arbitrary-resolution

U2 - 10.1017/S0013091518000901

DO - 10.1017/S0013091518000901

M3 - статья

VL - 62

SP - 817

EP - 836

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

IS - 3

ER -

ID: 43692515