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

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

doi:10.1080/00927870701665339

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

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

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引用

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.

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

要旨

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.