2007
Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket
BERING LARSEN, KlausZákladní údaje
Originální název
Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket
Název česky
Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket
Autoři
Vydání
Communications in Mathematical Physics, Berlin / Heidelberg, Springer, 2007, 0010-3616
Další údaje
Jazyk
angličtina
Typ výsledku
Článek v odborném periodiku
Obor
10303 Particles and field physics
Stát vydavatele
Německo
Utajení
není předmětem státního či obchodního tajemství
Odkazy
Impakt faktor
Impact factor: 2.070
Označené pro přenos do RIV
Ano
Kód RIV
RIV/00216224:14310/07:00021654
Organizační jednotka
Přírodovědecká fakulta
UT WoS
Klíčová slova anglicky
Batalin-Vilkovisky Algebra; Homotopy Lie Algebra; Koszul Bracket; Derived Bracket; Courant Bracket.
Štítky
Příznaky
Mezinárodní význam, Recenzováno
Změněno: 17. 3. 2019 17:09, doc. Klaus Bering Larsen, Ph.D.
V originále
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.
Česky
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.
Návaznosti
| MSM0021622409, záměr |
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