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Cohomology theories for homotopy algebras and noncommutative geometry

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Cohomology theories for homotopy algebras and noncommutative geometry. / Hamilton, Alastair; Lazarev, Andrey.
In: Algebraic and Geometric Topology, Vol. 9, No. 3, 2009, p. 1503-1583.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Hamilton, A & Lazarev, A 2009, 'Cohomology theories for homotopy algebras and noncommutative geometry', Algebraic and Geometric Topology, vol. 9, no. 3, pp. 1503-1583. https://doi.org/10.2140/agt.2009.9.1503

APA

Vancouver

Hamilton A, Lazarev A. Cohomology theories for homotopy algebras and noncommutative geometry. Algebraic and Geometric Topology. 2009;9(3):1503-1583. doi: 10.2140/agt.2009.9.1503

Author

Hamilton, Alastair ; Lazarev, Andrey. / Cohomology theories for homotopy algebras and noncommutative geometry. In: Algebraic and Geometric Topology. 2009 ; Vol. 9, No. 3. pp. 1503-1583.

Bibtex

@article{cfc822ec6af545289d26511846bb4b90,
title = "Cohomology theories for homotopy algebras and noncommutative geometry",
abstract = "This paper builds a general framework in which to study cohomology theories of strongly homotopy algebras, namely A∞–, C∞– and L∞–algebras. This framework is based on noncommutative geometry as expounded by Connes and Kontsevich. The developed machinery is then used to establish a general form of Hodge decomposition of Hochschild and cyclic cohomology of C∞–algebras. This generalises and puts in a conceptual framework previous work by Loday and Gerstenhaber–Schack.",
keywords = "infinity-algebra, cyclic cohomology , Harrison cohomology , symplectic structure , Hodge decomposition",
author = "Alastair Hamilton and Andrey Lazarev",
year = "2009",
doi = "10.2140/agt.2009.9.1503",
language = "English",
volume = "9",
pages = "1503--1583",
journal = "Algebraic and Geometric Topology",
issn = "1472-2747",
publisher = "Agriculture.gr",
number = "3",

}

RIS

TY - JOUR

T1 - Cohomology theories for homotopy algebras and noncommutative geometry

AU - Hamilton, Alastair

AU - Lazarev, Andrey

PY - 2009

Y1 - 2009

N2 - This paper builds a general framework in which to study cohomology theories of strongly homotopy algebras, namely A∞–, C∞– and L∞–algebras. This framework is based on noncommutative geometry as expounded by Connes and Kontsevich. The developed machinery is then used to establish a general form of Hodge decomposition of Hochschild and cyclic cohomology of C∞–algebras. This generalises and puts in a conceptual framework previous work by Loday and Gerstenhaber–Schack.

AB - This paper builds a general framework in which to study cohomology theories of strongly homotopy algebras, namely A∞–, C∞– and L∞–algebras. This framework is based on noncommutative geometry as expounded by Connes and Kontsevich. The developed machinery is then used to establish a general form of Hodge decomposition of Hochschild and cyclic cohomology of C∞–algebras. This generalises and puts in a conceptual framework previous work by Loday and Gerstenhaber–Schack.

KW - infinity-algebra

KW - cyclic cohomology

KW - Harrison cohomology

KW - symplectic structure

KW - Hodge decomposition

U2 - 10.2140/agt.2009.9.1503

DO - 10.2140/agt.2009.9.1503

M3 - Journal article

VL - 9

SP - 1503

EP - 1583

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

SN - 1472-2747

IS - 3

ER -