Examples of homotopy Lie algebras
Archivum Mathematicum (2009)
- Volume: 045, Issue: 4, page 265-277
- ISSN: 0044-8753
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topBering, Klaus, and Lada, Tom. "Examples of homotopy Lie algebras." Archivum Mathematicum 045.4 (2009): 265-277. <http://eudml.org/doc/250561>.
@article{Bering2009,
abstract = {We look at two examples of homotopy Lie algebras (also known as $L_\{\infty \}$ algebras) in detail from two points of view. We will exhibit the algebraic point of view in which the generalized Jacobi expressions are verified by using degree arguments and combinatorics. A second approach using the nilpotency of Grassmann-odd differential operators $\Delta $ to verify the homotopy Lie data is shown to produce the same results.},
author = {Bering, Klaus, Lada, Tom},
journal = {Archivum Mathematicum},
keywords = {homotopy Lie algebras; generalized Batalin-Vilkovisky algebras; Koszul brackets; higher antibrackets; homotopy Lie algebra; generalized Batalin-Vilkovisky algebra; Koszul brackets; higher antibrackets},
language = {eng},
number = {4},
pages = {265-277},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Examples of homotopy Lie algebras},
url = {http://eudml.org/doc/250561},
volume = {045},
year = {2009},
}
TY - JOUR
AU - Bering, Klaus
AU - Lada, Tom
TI - Examples of homotopy Lie algebras
JO - Archivum Mathematicum
PY - 2009
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 045
IS - 4
SP - 265
EP - 277
AB - We look at two examples of homotopy Lie algebras (also known as $L_{\infty }$ algebras) in detail from two points of view. We will exhibit the algebraic point of view in which the generalized Jacobi expressions are verified by using degree arguments and combinatorics. A second approach using the nilpotency of Grassmann-odd differential operators $\Delta $ to verify the homotopy Lie data is shown to produce the same results.
LA - eng
KW - homotopy Lie algebras; generalized Batalin-Vilkovisky algebras; Koszul brackets; higher antibrackets; homotopy Lie algebra; generalized Batalin-Vilkovisky algebra; Koszul brackets; higher antibrackets
UR - http://eudml.org/doc/250561
ER -
References
top- Batalin, I. A., Vilkovisky, G. A., Gauge algebra and quantization, Phys. Lett. 102B (1981), 27–31. (1981) MR0616572
- Bering, K., 10.1007/s00220-007-0278-3, Comm. Math. Phys. 274 (2007), 297–34. (2007) Zbl1146.17015MR2322905DOI10.1007/s00220-007-0278-3
- Bering, K., Damgaard, P. H., Alfaro, J., 10.1016/0550-3213(96)00401-4, Nuclear Phys. B 478 (1996), 459–504. (1996) Zbl0925.81398MR1420164DOI10.1016/0550-3213(96)00401-4
- Daily, M., Examples of and structures on , unpublished notes.
- Daily, M., Lada, T., A finite dimensional algebra example in gauge theory, Homotopy, Homology and Applications 7 (2005), 87–93. (2005) Zbl1075.18011MR2156308
- Lada, T., Markl, M., 10.1080/00927879508825335, Comm. Algebra 23 (1995), 2147–2161. (1995) Zbl0999.17019MR1327129DOI10.1080/00927879508825335
- Lada, T., Stasheff, J. D., 10.1007/BF00671791, Internat. J. Theoret. Phys. 32 (1993), 1087–1103. (1993) Zbl0824.17024MR1235010DOI10.1007/BF00671791
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