On the non-Koszulity of ternary partially associative operad

Abstract. The classification of complex of real finite dimensional Lie algebras which are not semi simple is still in its early stages. For example the nilpotent Lie algebras are classified only up to the dimension 7. Moreover, to recognize a given Lie algebra in a classification list is not so easy. In this work we propose a different approach to this problem. We determine families for some fixed invariants, the classification follows by a deformation process or contraction process. We focus on the case of 2 and 3-step nilpotent Lie algebras. We describe in both cases a deformation cohomology for this type of algebras and the algebras which are rigid regarding this cohomology. Other p-step nilpotent Lie algebras are obtained by contraction of the rigid ones.

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“…for any x, y, z, t, u. The corresponding operad is studied in [12] and [15]. Let g be a Lie algebra.…”

Section: Examplesmentioning

confidence: 99%

k-step nilpotent Lie algebras

Goze

Remm

2015

Georgian Mathematical Journal

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“…The cohomology of totally associative n-ary algebras was studied by Carlsson through the embedding (see [10]). In [3], the first and second authors extended the 1-parameter formal deformation theory to ternary algebras of associative type and in [4] they discussed their cohomologies adapted to deformations, see also [39,30,73]. The Hom-algebras structures arose first in quasi-deformation of Lie algebras of vector fields.…”

mentioning

confidence: 99%

Generalization of n-ary Nambu algebras and beyond

Ataguema

Makhlouf

Silvestrov

2009

Journal of Mathematical Physics

121

179

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Abstract. The aim of this paper is to introduce n-ary Hom-algebra structures generalizing the n-ary algebras of Lie type enclosing n-ary Nambu algebras, n-ary Nambu-Lie algebras, n-ary Lie algebras, and n-ary algebras of associative type enclosing n-ary totally associative and n-ary partially associative algebras. Also, we provide a way to construct examples starting from an n-ary algebra and an n-ary algebras endomorphism. Several examples could be derived using this process.

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“…for any x, y, z, t, u. The corresponding operad is studied in [12], [13], [17] and [15]. Let g be a Lie algebra.…”

Section: Cubic Associative Lie Multiplicationmentioning

confidence: 99%