We depict the weight diagrams of basic and adjoint representations of complex simple Lie algebras/algebraic groups and describe some of their uses.

In this paper we consider Z-actions, d ≥ 1, by automorphisms of compact connected abelian groups which contain at least one expansive automorphism (such actions are called algebraic Z-actions of expansive rank one). If α is such a Z-action on an infinite compact connected abelian group X, then every expansive element α of this action has a dense group ∆αn(X) of homoclinic points. For different ...

Following recent advances in largeN matrix mechanics, I discuss here the free (Cuntz) algebraic formulation of the large N limit of two-dimensional conformal field theories of chiral adjoint fermions and bosons. One of the central results is a new affine free algebra which describes a large N limit of su(N) affine Lie algebra. Other results include the associated free-algebraic partition functi...

We show that in a symmetric m-convex algebra without algebraic zero divisors, any self-adjoint and invertible element is either positive or negative. As a consequence we obtain that a symmetric m-convex algebra containing no algebraic zero divisors and for which every positive element has a positive square root is isomorphic to C + Rad(A).

We show that in a symmetric m-convex algebra without algebraic zero divisors, any self-adjoint and invertible element is either positive or negative. As a consequence we obtain that a symmetric m-convex algebra containing no algebraic zero divisors and for which every positive element has a positive square root is isomorphic to C + Rad(A).

This paper is devoted to the generalization of construction a Jordan algebra Lie and known theorems on local finite-dimensionality PI-algebras with an algebraic adjoint representation Mal’tsev algebras.

The adjoint of a composition operator on H2 induced by a rational function is computed explicitly as a multiple valued weighted composition operator. This computation is based on an expression for the adjoint of a composition operator on the Hardy space, and many other functional Hilbert spaces, as an integral operator. The formula for the adjoint of a composition operator on H2 with rational s...

In this short paper, we use Tannakian reconstruction techniques to prove a result that explains how reconstruct the stacky approach de Rham cohomology from classical theory of algebraic via an application adjoint functor theorem.

An e4cient numerical method for sensitivity computation of large-scale di$erential-algebraic systems is developed based on the adjoint method. Issues that are critical for the implementation are addressed. Complexity analysis and numerical results demonstrate that the adjoint sensitivity method is advantageous over the forward sensitivity method for applications with a large number of sensitivi...

The paper discusses the questions of coincidence basic nil-radicals on classes algebraic Lie algebras and proves local finite-dimensionality with an adjoint representation bounded degree over fields sufficiently large positive characteristic.