ar X iv : 0 90 3 . 54 33 v 1 [ m at h . Q A ] 3 1 M ar 2 00 9 EXAMPLES OF HOMOTOPY LIE ALGEBRAS
نویسنده
چکیده
We look at two examples of homotopy Lie algebras (also known as L∞ 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 ∆ to verify the homotopy Lie data is shown to produce the same results.
منابع مشابه
ar X iv : m at h / 06 11 38 6 v 1 [ m at h . R A ] 1 3 N ov 2 00 6 Quasi Q n - filiform Lie algebras ∗
In this paper we explicitly determine the derivation algebra, automorphism group of quasi Qn-filiform Lie algebras, and applying some properties of root vector decomposition we obtain their isomorphism theorem. AMS Classification: 17B05; 17B30
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We construct the finite dimensional simple integral modules for the (degenerate) affine Hecke-Clifford algebra (AHCA), H aff Cℓ (d). Our construction includes an analogue of Zelevin-sky's segment representations, a complete combinatorial description of the simple calibrated H aff Cℓ (d)-modules, and a classification of the simple integral H aff Cℓ (d)-modules. Our main tool is an analogue of th...
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