Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F07%3A00021654" target="_blank" >RIV/00216224:14310/07:00021654 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket

Popis výsledku v původním jazyce

We consider two different constructions of higher brackets. First, based on a Grassmann-odd, nilpotent Delta operator, we define a non-commutative generalization of the higher Koszul brackets, which are used in a generalized Batalin-Vilkovisky algebra,and we show that they form a homotopy Lie algebra. Secondly, we investigate higher, so-called derived brackets built from symmetrized, nested Lie brackets with a fixed nilpotent Lie algebra element Q. We find the most general Jacobi-like identity that such a hierarchy satisfies. The numerical coefficients in front of each term in these generalized Jacobi identities are related to the Bernoulli numbers. We suggest that the definition of a homotopy Lie algebra should be enlarged to accommodate this important case. Finally, we consider the Courant bracket as an example of a derived bracket. We extend it to the "big bracket" of exterior forms and poly-vectors, and give closed formulas for the higher Courant brackets.

Název v anglickém jazyce

Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket

Popis výsledku anglicky

We consider two different constructions of higher brackets. First, based on a Grassmann-odd, nilpotent Delta operator, we define a non-commutative generalization of the higher Koszul brackets, which are used in a generalized Batalin-Vilkovisky algebra,and we show that they form a homotopy Lie algebra. Secondly, we investigate higher, so-called derived brackets built from symmetrized, nested Lie brackets with a fixed nilpotent Lie algebra element Q. We find the most general Jacobi-like identity that such a hierarchy satisfies. The numerical coefficients in front of each term in these generalized Jacobi identities are related to the Bernoulli numbers. We suggest that the definition of a homotopy Lie algebra should be enlarged to accommodate this important case. Finally, we consider the Courant bracket as an example of a derived bracket. We extend it to the "big bracket" of exterior forms and poly-vectors, and give closed formulas for the higher Courant brackets.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BE - Teoretická fyzika

OECD FORD obor

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Projekt

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Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2007

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Communications in Mathematical Physics

ISSN

0010-3616

e-ISSN

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Svazek periodika

274

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

45

Strana od-do

297-341

Kód UT WoS článku

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EID výsledku v databázi Scopus

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