Comparison of 3-dimensional Z-graded and Z2-graded LInfinity algebras

Daily, M.; Fialowski, A.; Penkava, M.

doi:10.1080/00927870701665339

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Journal Article

Comparison of 3-dimensional Z-graded and Z2-graded LInfinity algebras

MPS-Authors

Daily, M.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

External Resource

No external resources are shared

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

There are no public fulltexts stored in PuRe

Supplementary Material (public)

There is no public supplementary material available

Citation

Daily, M., Fialowski, A., & Penkava, M. (2008). Comparison of 3-dimensional Z-graded and Z2-graded LInfinity algebras. Communications in Algebra, 36(1), 232-257. doi:10.1080/00927870701665339.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-638D-C

Abstract

This article explores L∞ structures on 3-dimensional vector spaces with both Zopf- and Zopf2-gradings. Since Zopf-graded L∞ algebras are special cases of Zopf2-graded algebras in the induced Zopf2-grading, there are generally fewer Zopf-graded L∞ structures on a given space. However, degree zero automorphisms (rather than even automorphisms) determine equivalence in a Zopf-graded space. We therefore find nontrivial examples in which the map from the Zopf-graded moduli space to the Zopf2-graded moduli space is bijective, injective but not surjective, or surjective but not injective. Additionally, we study how the codifferentials in the moduli spaces deform into other nonequivalent codifferentials.