Attributes | Values |
---|
rdf:type
| |
Description
| - 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 %22big bracket%22 of exterior forms and poly-vectors, and give closed formulas for the higher Courant brackets.
- 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 %22big bracket%22 of exterior forms and poly-vectors, and give closed formulas for the higher Courant brackets. (en)
|
Title
| - Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket
- Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket (en)
|
skos:prefLabel
| - Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket
- Non-Commutative Batalin-Vilkovisky Algebras, Homotopy Lie Algebras and the Courant Bracket (en)
|
skos:notation
| - RIV/00216224:14310/07:00021654!RIV10-MSM-14310___
|
http://linked.open...avai/riv/aktivita
| |
http://linked.open...avai/riv/aktivity
| |
http://linked.open...iv/cisloPeriodika
| |
http://linked.open...vai/riv/dodaniDat
| |
http://linked.open...aciTvurceVysledku
| |
http://linked.open.../riv/druhVysledku
| |
http://linked.open...iv/duvernostUdaju
| |
http://linked.open...titaPredkladatele
| |
http://linked.open...dnocenehoVysledku
| |
http://linked.open...ai/riv/idVysledku
| - RIV/00216224:14310/07:00021654
|
http://linked.open...riv/jazykVysledku
| |
http://linked.open.../riv/klicovaSlova
| - Batalin-Vilkovisky Algebra; Homotopy Lie Algebra; Koszul Bracket; Derived Bracket; Courant Bracket. (en)
|
http://linked.open.../riv/klicoveSlovo
| |
http://linked.open...odStatuVydavatele
| - DE - Spolková republika Německo
|
http://linked.open...ontrolniKodProRIV
| |
http://linked.open...i/riv/nazevZdroje
| - Communications in Mathematical Physics
|
http://linked.open...in/vavai/riv/obor
| |
http://linked.open...ichTvurcuVysledku
| |
http://linked.open...cetTvurcuVysledku
| |
http://linked.open...UplatneniVysledku
| |
http://linked.open...v/svazekPeriodika
| |
http://linked.open...iv/tvurceVysledku
| |
http://linked.open...ain/vavai/riv/wos
| |
http://linked.open...n/vavai/riv/zamer
| |
issn
| |
number of pages
| |
http://localhost/t...ganizacniJednotka
| |