| Title:
|
Derivations of homotopy algebras (English) |
| Author:
|
Lada, Tom |
| Author:
|
Tolley, Melissa |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
49 |
| Issue:
|
5 |
| Year:
|
2013 |
| Pages:
|
309-315 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
$L_\infty $ algebra |
| Keyword:
|
$A_\infty $ algebra |
| Keyword:
|
strong homotopy derivation |
| MSC:
|
18G55 |
| idZBL:
|
Zbl 06383793 |
| idMR:
|
MR3159330 |
| DOI:
|
10.5817/AM2013-5-309 |
| . |
| Date available:
|
2014-01-16T11:20:09Z |
| Last updated:
|
2015-03-19 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143555 |
| . |
| Reference:
|
[1] Allocca, M., Lada, T.: A finite dimensional $A_\infty $ algebra example.Georgian Math. J. 12 (10) (2010), 1–12. Zbl 1207.18014, MR 2640644 |
| Reference:
|
[2] Kajiura, H., Stasheff, J.: Homotopy algebras inspired by classical open–closed string field theory.Comm. Math. Phys. 263 (3) (2006), 553–581. Zbl 1125.18012, MR 2211816, 10.1007/s00220-006-1539-2 |
| Reference:
|
[3] Lada, T.: Commutators of $A_\infty $ structures.Contemporary Mathematics, 1999, pp. 227–233. Zbl 0940.16015 |
| Reference:
|
[4] Lada, T., Markl, M.: Strongly homotopy Lie algebras.Comm. Algebra 23 (6) (1995), 2147–2161. Zbl 0999.17019, 10.1080/00927879508825335 |
| Reference:
|
[5] Lada, T., Stasheff, J.: Introduction to SH Lie algebras for physicists.Internat. J. Theoret. Phys. 32 (7) (1993), 1087–1103. Zbl 0824.17024, 10.1007/BF00671791 |
| Reference:
|
[6] Stasheff, J.: Homotopy associativity of H-spaces II.Trans. Amer. Math. Soc. 108 (1963), 293–312. |
| Reference:
|
[7] Tolley, M.: The connections between $A_\infty $ and $L_\infty $ algebras.Ph.D. thesis, NCSU, 2013. |
| . |
