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Keywords:
homotopy Lie algebras; generalized Batalin-Vilkovisky algebras; Koszul brackets; higher antibrackets
homotopy Lie algebras; generalized Batalin-Vilkovisky algebras; Koszul brackets; higher antibrackets
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.
References:
[1] Batalin, I. A., Vilkovisky, G. A.: Gauge algebra and quantization. Phys. Lett. 102B (1981), 27–31. MR 0616572
[2] Bering, K.: Non-commutative Batalin-Vilkovisky algebras, homotopy Lie algebras and the Courant bracket. Comm. Math. Phys. 274 (2007), 297–34. DOI 10.1007/s00220-007-0278-3 | MR 2322905 | Zbl 1146.17015
[3] Bering, K., Damgaard, P. H., Alfaro, J.: Algebra of higher antibrackets. Nuclear Phys. B 478 (1996), 459–504. DOI 10.1016/0550-3213(96)00401-4 | MR 1420164 | Zbl 0925.81398
[4] Daily, M.: Examples of $L_m$ and $L_\infty $ structures on $V_0\oplus V_1$. unpublished notes.
[5] Daily, M., Lada, T.: A finite dimensional $L_\infty $ algebra example in gauge theory. Homotopy, Homology and Applications 7 (2005), 87–93. MR 2156308 | Zbl 1075.18011
[6] Lada, T., Markl, M.: Strongly homotopy Lie algebras. Comm. Algebra 23 (1995), 2147–2161. DOI 10.1080/00927879508825335 | MR 1327129 | Zbl 0999.17019
[7] Lada, T., Stasheff, J. D.: Introduction to sh Lie algebras for physicists. Internat. J. Theoret. Phys. 32 (1993), 1087–1103. DOI 10.1007/BF00671791 | MR 1235010 | Zbl 0824.17024
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