BERING LARSEN, Klaus. Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket. Communications in Mathematical Physics. Berlin / Heidelberg: Springer, 2007, roč. 274, č. 2, s. 297-341. ISSN 0010-3616. Dostupné z: https://dx.doi.org/10.1007/s00220-007-0278-3.
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Základní 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 BERING LARSEN, Klaus (208 Dánsko, garant, domácí).
Vydání Communications in Mathematical Physics, Berlin / Heidelberg, Springer, 2007, 0010-3616.
Další údaje
Originální jazyk angličtina
Typ výsledku Článek v odborném periodiku
Obor 10303 Particles and field physics
Stát vydavatele Německo
Utajení není předmětem státního či obchodního tajemství
WWW URL
Impakt faktor Impact factor: 2.070
Kód RIV RIV/00216224:14310/07:00021654
Organizační jednotka Přírodovědecká fakulta
Doi http://dx.doi.org/10.1007/s00220-007-0278-3
UT WoS 000248134900002
Klíčová slova anglicky Batalin-Vilkovisky Algebra; Homotopy Lie Algebra; Koszul Bracket; Derived Bracket; Courant Bracket.
Štítky Batalin-Vilkovisky Algebra, Courant Bracket., Derived Bracket, Homotopy Lie Algebra, Koszul Bracket
Příznaky Mezinárodní význam, Recenzováno
Změnil Změnil: doc. Klaus Bering Larsen, Ph.D., učo 203385. Změněno: 17. 3. 2019 17:09.
Anotace
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.
Anotace 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, záměrNázev: Matematické struktury a jejich fyzikální aplikace
Investor: Ministerstvo školství, mládeže a tělovýchovy ČR, Matematické struktury a jejich fyzikální aplikace
VytisknoutZobrazeno: 19. 9. 2024 08:48