We consider the Norton algebra associated with a Q -polynomial primitive idempotent of adjacency matrix for distance-regular graph. obtain formula product that we find attractive.

Let U be an open relatively compact subanalytic subset of a real analytic manifold. We show that there exists a finite linear covering (in the sense of Guillermou and Schapira) of U by subanalytic open subsets of U homeomorphic to a unit ball. We also show that the algebra of open relatively compact subanalytic subsets of a real analytic manifold is generated by subsets subanalytically and bi-l...

Let G be a reductive connected linear algebraic group over an algebraically closed field of positive characteristic and let g be its Lie algebra. First we correct and generalise a well-known result about the Picard group of G. Then we prove that, if the derived group is simply connected and g satisfies a mild condition, the algebra K[G] of regular functions on G that are invariant under the act...

Some unexpected properties of the cubic algebra generated by the covariant derivatives of a generic Yang-Mills connection over the (s+ 1)-dimensional pseudo euclidean space are pointed out. This algebra is Gorenstein and Koszul of global dimension 3 but except for s = 1 (i.e. in the 2-dimensional case) where it is the universal enveloping algebra of the Heisenberg Lie algebra and is a cubic Art...

Motivated by the construction of invariants of links in 3-space, we study spin models on graphs for which all edge weights (considered as matrices) belong to the Bose-Mesner algebra of some association scheme. We show that for series-parallel graphs the computation of the partition function can be performed by using seriesparallel reductions of the graph appropriately coupled with operations in...

In the present paper for a large family of topological semigroups, namely foundation semigroups, for which topological groups and discrete semigroups are elementary examples, it is shown that ?(S) is the dual of a function algebra.

We prove a Lusternik-Schnirelmann type theorem for <em>C</em><sup>1</sup>- function φ : M → R, where is connected infinite dimensional Frechet manifold of class <em>C</em><sup>1</sup>. To this end, in context we the so-called Deformation Lemma and by using it derive result generalizing Minimax Principle.