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Article

Keywords:
$L_\infty $ algebra; $A_\infty $ algebra; strong homotopy derivation
Summary:
We recall the definition of strong homotopy derivations of $A_\infty $ algebras and introduce the corresponding definition for $L_\infty $ algebras. We define strong homotopy inner derivations for both algebras and exhibit explicit examples of both.
References:
[1] Allocca, M., Lada, T.: A finite dimensional $A_\infty $ algebra example. Georgian Math. J. 12 (10) (2010), 1–12. MR 2640644 | Zbl 1207.18014
[2] Kajiura, H., Stasheff, J.: Homotopy algebras inspired by classical open–closed string field theory. Comm. Math. Phys. 263 (3) (2006), 553–581. DOI 10.1007/s00220-006-1539-2 | MR 2211816 | Zbl 1125.18012
[3] Lada, T.: Commutators of $A_\infty $ structures. Contemporary Mathematics, 1999, pp. 227–233. Zbl 0940.16015
[4] Lada, T., Markl, M.: Strongly homotopy Lie algebras. Comm. Algebra 23 (6) (1995), 2147–2161. DOI 10.1080/00927879508825335 | Zbl 0999.17019
[5] Lada, T., Stasheff, J.: Introduction to SH Lie algebras for physicists. Internat. J. Theoret. Phys. 32 (7) (1993), 1087–1103. DOI 10.1007/BF00671791 | Zbl 0824.17024
[6] Stasheff, J.: Homotopy associativity of H-spaces II. Trans. Amer. Math. Soc. 108 (1963), 293–312.
[7] Tolley, M.: The connections between $A_\infty $ and $L_\infty $ algebras. Ph.D. thesis, NCSU, 2013.
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