Let L be a Lie algebra over arbitary field k with dim L =3 and dim L =2. All solutions of constant classical YangBaxter equation (CYBE) in Lie algebra L are obtained and the necessary conditions which (L, [ ],∆r, r) is a coboundary ( or triangular ) Lie bialgebra are given. AMS Subject Classification:16; 17; 81

We show that the multiplier algebra of the Fourier algebra on a locally compact group G can be isometrically represented on a direct sum on non-commutative L spaces associated to the right von Neumann algebra of G. If these spaces are given their canonical Operator space structure, then we get a completely isometric representation of the completely bounded multiplier algebra. We make a careful ...

Let L be a Lie algebra with the universal enveloping algebra U(L). The augmentation ideal ω(L) of U(L) is the associative ideal of U(L) generated by L. Let S be a subalgebra of L and n a positive integer. In this paper we prove that L ∩ ω(L)ω(S) = γn+2(S) + γn+1(S∩γ2(L)), where γn+2(S) is the (n+2) term of the lower central series of S.

Let L be a Lie algebra over arbitrary field k with dim L =3 and dim L =2. All solutions of constant classical YangBaxter equation (CYBE) in Lie algebra L are obtained and the necessary conditions which (L, [ ],∆r, r) is a coboundary ( or triangular ) Lie bialgebra are given. AMS Subject Classification:16; 17; 81

We show that the Faddeev-Pyatov SL q (N) differential algebra [1] is a subalgebra of the GL q (N) differential algebra constructed by Schupp, Watts and Zumino [2]. In the paper [1], the bicovariant differential algebra on SL q (N) (see below (10), (11)) with generators {T ij , L ij , ˜ Ω ij } i, j = 1,. .. N has been constructed. The elements T ij are generators of the algebra F un(SL q (N)), w...

Let B be a representation-finite C-algebra. The Z-Lie algebra L(B) associated with B has been defined by Ch. Riedtmann in [17]. If B is representation-directed there is another Z-Lie algebra associated with B defined by C. M. Ringel in [20] and denoted by K(B). We prove that the Lie algebras L(B) and K(B) are isomorphic for any representation-directed C-algebra B. 2000 Mathematics Subject Class...

Let H be a finitely-generated free abelian group and L(H) the graded free Lie algebra on H . There is a natural homomorphism H ⊗ L(H)→ L(H) defined by bracketing, whose kernel is denoted D(H). If H supports a non-singular symplectic form, eg H = H1(Σ), where Σ is a closed orientable surface, with symplectic basis {xi, yi}, then D(H) is, in fact, a Lie algebra. It can be identified with the Lie ...

The Wahlquist-Estabrook prolongation method allows to obtain for some PDEs a Lie algebra that is responsible for Lax pairs and Bäcklund transformations of certain type. We study the Wahlquist-Estabrook algebra of the n-dimensional generalization of the Landau-Lifshitz equation and construct an epimorphism from this algebra onto an infinite-dimensional quasigraded Lie algebra L(n) of certain mat...

We construct a functor from the category of modules over the trigonometric (resp. rational) Cherednik algebra of type gll to the category of integrable modules of level l over a Yangian for the loop algebra sln (resp. over a subalgebra of this Yangian called the Yangian deformed double loop algebra) and we establish that it is an equivalence of categories if l + 2 < n.

The sequent calculus sL for the Lambek calculus L ([2]) has no structural rules. Interestingly, sL is equivalent to a multimodal calculus mL, which consists of the nonassociative Lambek calculus with the structural rule of associativity. This paper proves that the sequent calculus or hypersequent calculus hD of the discontinuous Lambek calculus1 ([7], [4] and [8]), which like sL has no structur...