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Involutive A-infinity algebras and dihedral cohomology

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Involutive A-infinity algebras and dihedral cohomology. / Braun, Christopher.
In: Journal of Homotopy and Related Structures, Vol. 9, No. 2, 10.2014, p. 317-337.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Braun, C 2014, 'Involutive A-infinity algebras and dihedral cohomology', Journal of Homotopy and Related Structures, vol. 9, no. 2, pp. 317-337. https://doi.org/10.1007/s40062-013-0030-y

APA

Braun, C. (2014). Involutive A-infinity algebras and dihedral cohomology. Journal of Homotopy and Related Structures, 9(2), 317-337. https://doi.org/10.1007/s40062-013-0030-y

Vancouver

Braun C. Involutive A-infinity algebras and dihedral cohomology. Journal of Homotopy and Related Structures. 2014 Oct;9(2):317-337. Epub 2013 Apr 23. doi: 10.1007/s40062-013-0030-y

Author

Braun, Christopher. / Involutive A-infinity algebras and dihedral cohomology. In: Journal of Homotopy and Related Structures. 2014 ; Vol. 9, No. 2. pp. 317-337.

Bibtex

@article{0760202baee9470fb991eecbaa36145f,
title = "Involutive A-infinity algebras and dihedral cohomology",
abstract = "We define and study the cohomology theories associated to A-infinity algebras and cyclic A-infinity algebras equipped with an involution, generalising dihedral cohomology to the A-infinity context. Such algebras arise, for example, as unoriented versions of topological conformal field theories. It is well known that Hochschild cohomology and cyclic cohomology govern, in a precise sense, the deformation theory of A-infinity algebras and cyclic A-infinity algebras and we give analogous results for the deformation theory in the presence of an involution. We also briefly discuss generalisations of these constructions and results to homotopy algebras over Koszul operads, such as L-infinity algebras or C-infinity algebras equipped with an involution.",
keywords = "A ∞ -algebras , Involution, Dihedral cohomology, Deformation theory, Operads ",
author = "Christopher Braun",
note = "Date of Acceptance: 05/04/2013 The final publication is available at Springer via http://dx.doi.org/10.1007/s40062-013-0030-y",
year = "2014",
month = oct,
doi = "10.1007/s40062-013-0030-y",
language = "English",
volume = "9",
pages = "317--337",
journal = "Journal of Homotopy and Related Structures",
issn = "2193-8407",
publisher = "Springer Science + Business Media",
number = "2",

}

RIS

TY - JOUR

T1 - Involutive A-infinity algebras and dihedral cohomology

AU - Braun, Christopher

N1 - Date of Acceptance: 05/04/2013 The final publication is available at Springer via http://dx.doi.org/10.1007/s40062-013-0030-y

PY - 2014/10

Y1 - 2014/10

N2 - We define and study the cohomology theories associated to A-infinity algebras and cyclic A-infinity algebras equipped with an involution, generalising dihedral cohomology to the A-infinity context. Such algebras arise, for example, as unoriented versions of topological conformal field theories. It is well known that Hochschild cohomology and cyclic cohomology govern, in a precise sense, the deformation theory of A-infinity algebras and cyclic A-infinity algebras and we give analogous results for the deformation theory in the presence of an involution. We also briefly discuss generalisations of these constructions and results to homotopy algebras over Koszul operads, such as L-infinity algebras or C-infinity algebras equipped with an involution.

AB - We define and study the cohomology theories associated to A-infinity algebras and cyclic A-infinity algebras equipped with an involution, generalising dihedral cohomology to the A-infinity context. Such algebras arise, for example, as unoriented versions of topological conformal field theories. It is well known that Hochschild cohomology and cyclic cohomology govern, in a precise sense, the deformation theory of A-infinity algebras and cyclic A-infinity algebras and we give analogous results for the deformation theory in the presence of an involution. We also briefly discuss generalisations of these constructions and results to homotopy algebras over Koszul operads, such as L-infinity algebras or C-infinity algebras equipped with an involution.

KW - A ∞ -algebras

KW - Involution

KW - Dihedral cohomology

KW - Deformation theory

KW - Operads

U2 - 10.1007/s40062-013-0030-y

DO - 10.1007/s40062-013-0030-y

M3 - Journal article

VL - 9

SP - 317

EP - 337

JO - Journal of Homotopy and Related Structures

JF - Journal of Homotopy and Related Structures

SN - 2193-8407

IS - 2

ER -