Polynomial detection of matrix subalgebras

Polynomial Detection of Matrix Subalgebras

The double Capelli polynomial of total degree 2t is

Differential Polynomial Rings of Triangular Matrix Rings

Quasi-orthogonal Subalgebras of Matrix Algebras@

In the theory of quantum mechanics, an n-level system is described by the algebra Mn =Mn(C) of n× n complex matrices. The matrix algebra of a composite system consisting of an n-level and an m-level system is Mn ⊗Mm ≃ Mnm. A subalgebra of Mk corresponds to a subsystem of a k-level quantum system. In this paper, subalgebras contain the identity and are closed under the adjoint operation of matri...

Maximal Subalgebras of Matrix Lie Superalgebras

Dynkin’s classification of maximal subalgebras of simple finite dimensional complex Lie algebras is generalized to matrix Lie superalgebras, i.e., the Lie subsuperalgebras of gl(p|q).

Algebraic adjoint of the polynomials-polynomial matrix multiplication

This paper deals with a result concerning the algebraic dual of the linear mapping defined by the multiplication of polynomial vectors by a given polynomial matrix over a commutative field