A basic problem in the theory of Lie algebra extensions concerns a given homomorphism x of a Lie algebra L into the Lie algebra of outer derivations of a Lie algebra B . In analogy with the theory of group extensions, Mori and HochschiId developed the concept of an obstruction to x being the homomorphism defined by some Lie algebra extension of B by L . This note considers an alternative approa...

The BH n (l; m) algebra is deened by two sets of generators one of which satisfy the relations of the braid group and the other the relations of the Hecke algebra of projectors.These algebras are then combined by additional relations in a way which generalize the Birman-Wenzl algebra C n (l; m). In this paper we Yang-Baxterize the algebra BH and compute solutions of the Yang-Baxter equation.The...

Inspired by [3] we introduce the concept of extended Hopf algebra and consider their cyclic cohomology in the spirit of Connes-Moscovici [3, 4, 5]. Extended Hopf algebras are closely related, but different from, Hopf algebroids. Their definition is motivated by attempting to define cyclic cohomology of Hopf algebroids in general. Many of Hopf algebra like structures, including the Connes-Moscov...

Abstract. In this paper we investigate Lie bialgebra structures on a twisted Schrödinger-Virasoro type algebra L. All Lie bialgebra structures on L are triangular coboundary, which is different from the relative result on the original Schrödinger-Virasoro type Lie algebra. In particular, we find for this Lie algebra that there are more hidden inner derivations from itself to L⊗L and we develop ...

Let L be a completely valued nonarchimedean field and g a finite dimensional Lie algebra over L. We show that its hyperenveloping algebra F(g) agrees with its Arens-Michael envelope and, furthermore, is a stably flat completion of its universal enveloping algebra. As an application, we prove that the Taylor relative cohomology for the locally convex algebra F(g) is naturally isomorphic to the L...

For any BL-algebra L, we construct an associated lattice ordered Abelian group GL that coincides with the Chang’s `-group of an MV-algebra when the BL-algebra is an MValgebra. We prove that the Chang’s group of the MV-center of any BL-algebra L is a direct summand in GL. We also find a direct description of the complement S(L) of the Chang’s group of the MV-center in terms of the filter of dens...

Various algebraic structures have recently appeared in a parallel way in the framework of Hilbert schemes of points on a surface and respectively in the framework of equivariant K-theory [N1, Gr, S2, W], but direct connections are yet to be clarified to explain such a coincidence. We provide several non-trivial steps toward establishing our main conjecture on the isomorphism between the Hilbert...

To study power series generated by Lindenmayer systems we de ne L algebraic systems and series over arbitrary commutative semirings. We establish closure and xed point properties of L algebraic series. We show how the framework of L algebraic series can be used to de ne D0L, 0L, E0L, DT0L, T0L and ET0L power series. We generalize for power series the classical result stating that D0L languages ...

intimately connected with duality theory (the notation is that of [1]). In both cases the middle algebra is the closure of L(G) in the dual of the first algebra and also the predual of the third algebra (at least when G is amenable in the second case). Furthermore, the third algebra is closely connected with the multiplier algebra of the first algebra. For abelian groups, compact or discrete, V...