We compute the Yoneda extension algebra of GL2 over an algebraically closed field of characteristic p > 0. 1. Intro Let F be an algebraically closed field of characteristic p > 0. Let G = GL2(F ) denote the group of 2 × 2 invertible matrices over F . Let L denote a complete set of irreducible objects in the category G -mod of rational representations of G. The object of this paper is to give an...

In this paper we give an axiom system of a non-linear 4-valued logic which we call a de Morgan logic (ML), whose Lindenbaum algebra is the de Morgan algebra with implication (MI-algebra), and show that (1) For every MI-algebra L, there is a quotient MI-algebra L such that it is embeddable to the simplest 4-valued MI-algebra M = {0, a, b, 1}; (2) The Lindenbaum algebra of ML is the MI-algebra; (...

For any L ∞-algebra L we construct an A ∞-algebra structure on the symmetric coalgebra Sym * c (L) and prove that this structure satifies properties generalizing those of the usual universal enveloping algebra. We also obtain an invariant contracting homotopy one the cobar construction of a symmetric coalgebra, by relating it to the combinatorics of permutahedra and semistandard Young tableaux.

In the first two sections, we review the Block-Wilson-PremetStrade classification of restricted simple Lie algebras. In the third section, we compute their infinitesimal deformations. In the last section, we indicate some possible generalizations by formulating some open problems. 1. Restricted Lie algebras We fix a field F of characteristic p > 0 and we denote with Fp the prime field with p el...

The BH n (l, m) algebra is defined 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.Th...

Using the concept of (K,L)-eigenvector, we investigate structure max-min eigenspace associated with a given eigenvalue matrix in algebra (also known as fuzzy algebra). In our approach, is split into several regions according to order relations between and components x. The resulting theory (K,L)-eigenvectors, being based on fundamental results Gondran Minoux, allows describe whole explicitly mo...

Let A be an associative algebra over a field F of characteristic zero and let L Lie F. If acts on by derivations, then such action determines its universal enveloping U(L) in this case we refer to as with derivations or L-algebra. Here give characterization the ideal differential identities finite dimensional L-algebras corresponding sequence codimensions ${c_{n}^{L}} (A)$ , n ≥ 1, is polynomia...

A simple proof is given of Chen's and Grätzer's theorem, which gives a method to construct a Stone algebra from a Boolean algebra and a distributive lattice with 1 by certain connective conditions between the two given lattices. C. C. Chen and G. Grätzer [1] proved originally the Construction Theorem for Stone algebras. In [3] we proved by different method the Construction Theorem for a larger ...

We construct an $L_\infty$-algebra on the truncated canonical homology complex of a symplectic manifold, which naturally projects to universal central extension Lie algebra Hamiltonian vector fields.