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A Pre-Lie algebra is a vector space L endowed with a bilinear product * : L \times L to L satisfying the relation (x*y)*z-x*(y*z)= (x*z)*y-x*(z*y), for all x,y,z in L. We give an explicit combinatoria...
We construct representation theory of Lie algebras with filtrations. In this framework a classification of irreducible representations is obtained and spectra of some reducible representations are fou...
SK_1 and Lie Algebras     uniform group  Iwasawa algebra  SK1  Lie algebra       2011/9/23
Abstract: We investigate the vanishing of the group SK1(A(G)) for the Iwasawa algebra A(G) of a pro-p p-adic Lie group G (with p different from 2). We reduce this vanishing to a linear algebra problem...
Abstract: For a field K and directed graph E, we analyze those elements of the Leavitt path algebra L_K(E) which lie in the commutator subspace [L_K(E), L_K(E)]. This analysis allows us to give easily...
Abstract: In the note some construction of Lie algebras is introduced. It is proved that the construction has the same property as a well known wreath product of groups [1]: Any extension of groups ca...
Abstract: At the previous congress (CRM 6), we reviewed the construction of Yang-Baxter operators from associative algebras, and presented some (colored) bialgebras and Yang-Baxter systems related to ...
Abstract: We study $\mathbb Z$-graded modules of nonzero level with arbitrary weight multiplicities over Heisenberg Lie algebras and the associated generalized loop modules over affine Kac-Moody Lie a...
Abstract: In this paper, we find a criterium for universal equivalence of partially commutative Lie algebras whose defining graphs are trees. Besides, we obtain bases for partially commutative metabel...
Divergence-free Lie algebras (also known as the special Lie algebras of Cartan type) are Lie algebras of volume-preserving transformation groups. They are simple in generic case. Dokovic and Zhao fo...
In this paper, linear bases for the partially commutative Lie alge-bras are found. The method of the Gr¨obner–Shirshov bases is used.
The u-homology formulas for unitarizable modules at negative levels over classical Lie algebras of infinite rank of types gl(n), sp(2n) and so(2n) are obtained.As a consequence, we recover the Enright...
Given an element P(X1, . . . ,Xd) of the free Lie K-algebra Ld, for any Lie algebra g we can consider the induced polynomial map P : gd → g. Assuming that K is an arbitrary field of characteristic 6= ...
The goal of this paper is to present some results and (more importantly) state a number of conjectures suggesting that the representation theory of symplectic reflection algebras for wreath products c...
In prime characteristic we introduce the notion of restricted pre-Lie algebra. We prove in the pre-Lie context the analogue to Jacobson's theorem for restricted Lie algebras. In particular, we prove t...
We give sufficient conditions for the descent construction to be the universal central extension of a twisted form of a split simple Lie algebra over a ring. In particular, the universal central exten...

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