| Title:
|
Examples of homotopy Lie algebras (English) |
| Author:
|
Bering, Klaus |
| Author:
|
Lada, Tom |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
45 |
| Issue:
|
4 |
| Year:
|
2009 |
| Pages:
|
265-277 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
homotopy Lie algebras |
| Keyword:
|
generalized Batalin-Vilkovisky algebras |
| Keyword:
|
Koszul brackets |
| Keyword:
|
higher antibrackets |
| MSC:
|
17B55 |
| MSC:
|
18G55 |
| idZBL:
|
Zbl 1212.18015 |
| idMR:
|
MR2591681 |
| . |
| Date available:
|
2009-12-22T07:52:58Z |
| Last updated:
|
2013-09-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/137459 |
| . |
| Reference:
|
[1] Batalin, I. A., Vilkovisky, G. A.: Gauge algebra and quantization.Phys. Lett. 102B (1981), 27–31. MR 0616572 |
| Reference:
|
[2] Bering, K.: Non-commutative Batalin-Vilkovisky algebras, homotopy Lie algebras and the Courant bracket.Comm. Math. Phys. 274 (2007), 297–34. Zbl 1146.17015, MR 2322905, 10.1007/s00220-007-0278-3 |
| Reference:
|
[3] Bering, K., Damgaard, P. H., Alfaro, J.: Algebra of higher antibrackets.Nuclear Phys. B 478 (1996), 459–504. Zbl 0925.81398, MR 1420164, 10.1016/0550-3213(96)00401-4 |
| Reference:
|
[4] Daily, M.: Examples of $L_m$ and $L_\infty $ structures on $V_0\oplus V_1$.unpublished notes. |
| Reference:
|
[5] Daily, M., Lada, T.: A finite dimensional $L_\infty $ algebra example in gauge theory.Homotopy, Homology and Applications 7 (2005), 87–93. Zbl 1075.18011, MR 2156308 |
| Reference:
|
[6] Lada, T., Markl, M.: Strongly homotopy Lie algebras.Comm. Algebra 23 (1995), 2147–2161. Zbl 0999.17019, MR 1327129, 10.1080/00927879508825335 |
| Reference:
|
[7] Lada, T., Stasheff, J. D.: Introduction to sh Lie algebras for physicists.Internat. J. Theoret. Phys. 32 (1993), 1087–1103. Zbl 0824.17024, MR 1235010, 10.1007/BF00671791 |
| . |
