A norm inequality is proved for elements of a star algebra so that the algebra is noncommutative. In particular, a relation between maximal and minimal extensions of regular norm on a C∗-algebra is established.

In this article we will build a universal imbedding of a regular HomLie triple system into a Lie algebra and show that the category of regular Hom-Lie triple systems is equivalent to a full subcategory of pairs of Z2graded Lie algebras and Lie algebra automorphism, then finally give some characterizations of this subcategory.

We study combinatorial aspects of the representation theory of the 0-Hecke algebra Hn(0), a deformation of the group algebra of the symmetric group Sn. We study the action of Hn(0) on the polynomial ring in n variables. We show that the coinvariant algebra of this action naturally carries the regular representation of Hn(0), giving an analogue of the well-known result for the symmetric group by...

We show that the axioms of Weak Kleene Algebra (WKA) are sound and complete for the theory of regular expressions modulo simulation equivalence, assuming their completeness for monodic trees (as conjectured by Takai and Furusawa).

Let E be a set of inequalities between finite Σ-terms. Let Vω and Vr denote the varieties of all ω-continuous ordered Σ-algebras and regular ordered Σ-algebras satisfying E, respectively. We prove that the free Vr-algebra R(X) on generators X is the subalgebra of the corresponding free Vω-algebra Fω(X) determined by those elements of Fω(X) denoted by the regular Σ-coterms. We actually establish...

We present in this paper a road traffic model based on Petri nets and minplus algebra in order to study the fundamental traffic diagram of regular city (american like city). The obtained dynamic is simulated using an extension of the maxplus toolbox of Scilab able to simulate general Petri nets with negative multipliers. The Petri net model corresponding to an intersection with traffic lights i...

We construct the H-von Neumann regular radical for H-module algebras and show that it is an H-radical property. We obtain that the Jacobson radical of twisted graded algebra is a graded ideal. For twisted H-module algebra R, we also show that rj(R#σH) = rHj(R)#σH and the Jacobson radical of R is stable, when k is an algebraically closed field or there exists an algebraic closure F of k such tha...

In this paper I will provide a proof of the Gauss-Bonnet Theorem. I will start by briefly explaining regular surfaces and move on to the first and second fundamental forms. I will then discuss Gaussian curvature and geodesics. Finally, I will move on to the theorem itself, giving both a local and a global version of the Gauss-Bonnet theorem. For this paper, I will assume that the reader has a k...

Regular Lie groups are infinite dimensional Lie groups with the property that smooth curves in the Lie algebra integrate to smooth curves in the group in a smooth way (an ‘evolution operator’ exists). Up to now all known smooth Lie groups are regular. We show in this paper that regular Lie groups allow to push surprisingly far the geometry of principal bundles: parallel transport exists and fla...

Regular Lie groups are infinite dimensional Lie groups with the property that smooth curves in the Lie algebra integrate to smooth curves in the group in a smooth way (an ‘evolution operator’ exists). Up to now all known smooth Lie groups are regular. We show in this paper that regular Lie groups allow to push surprisingly far the geometry of principal bundles: parallel transport exists and fla...