Related papers: T-ideals of Cayley Hamilton algebras
We develop the general Theory of Cayley Hamilton algebras using norms and compare with the approach, valid only in characteristic 0, using traces and presented in a previous paper $T$-ideals of Cayley Hamilton algebras, 2020,…
A subalgebra B of a Lie algebra L is called a c-ideal of L if there is an ideal C of L such that L = B + C and B \cap C \leq B_L, where B_L is the largest ideal of $L$ contained in B. This is analogous to the concept of c-normal subgroup,…
Starting from the expression for the superdeterminant of (xI-M), where M is an arbitrary supermatrix, we propose a definition for the corresponding characteristic polynomial and we prove that each supermatrix satisfies its characteristic…
The classical Cayley-Hamilton identities are generalized to quantum matrix algebras of the GL(m|n) type.
We prove that the lattice of ideals of an arbitrary $L$-algebra is distributive. As a consequence, a spectral theory applies with no restriction. We also study the spectrum (i.e. the set of prime ideals) of $L$-algebras and characterize…
We develop a theory of semialgebra Grassmann triples via Hasse-Schmidt derivations, which formally generalizes results such as the Cayley-Hamilton theorem in linear algebra, thereby providing a unified approach to classical linear algebra…
We present an overview of characteristic identities for Lie algebras and superalgebras. We outline methods that employ these characteristic identities to deduce matrix elements of finite dimensional representations. To demonstrate the…
We associate to outer automorphisms of generalized Kac-Moody algebras generalized character-valued indices, the twining characters. A character formula for twining characters is derived which shows that they coincide with the ordinary…
This article first introduces the concept of a general pseudo-homogeneous triangular norm. It then gives some properties of general pseudo-homogeneous triangular norms. Finally, it characterizes all general pseudo-homogeneous triangular…
We develop a method to construct algebraic invariants for hypermatrices. We then construct hyperdeterminants and exhibit a generalization of the Cayley-Hamilton theorem for hypermatrices.
A classification up to automorphism of the inner ideals of the real finite-dimensional simple Lie algebras is given, jointly with precise descriptions in the case of the exceptional Lie algebras.
We present two hypermatrix formulations of the Cayley Hamilton theorem. One of the proposed formulation naturally extends to hypermatrices the combinatorial interpretations of the classical Cayley Hamilton theorem. We conclude by discussing…
A subalgebra S of a Leibniz algebra L is called self-idealizing in L if it coincides with its idealizer IL(S). In this paper we study the structure of Leibniz algebras, whose subalgebras are either ideals or self-idealizing.
Let $F$ be an algebraically closed field of characteristic zero and let $G$ be a finite group. We consider graded Verbally prime $T$-ideals in the free $G$-graded algebra. It turns out that equivalent definitions in the ordinary case (i.e.…
We establish the analogue of the Cayley--Hamilton theorem for the quantum matrix algebras of the symplectic type.
We initiate a study on a range of new generalized derivations of finite-dimensional Lie algebras over an algebraically closed field of characteristic zero. This new generalization of derivations has an analogue in the theory of associative…
In this paper, we classify all Leavitt path algebras which have the property that every Lie ideal is an ideal. As an application, we show that Leavitt path algebras with this property provide a class of locally finite, infinite-dimensional…
In this paper we discuss the minimal Cayley Hamilton norm for a finite dimensional algebra over a field $F$ based on a paper by Skip Garibaldi
In 1970 Vaughan-Lee established that over an infinite field of characteristic two the ideal T[gl(2)] of all polynomial identities for the Lie algebra gl(2) is not finitely generated as a T-ideal. But a generating set for this ideal of…
Ideals generated by adjacent 2-minors are studied. First, the problem when such an ideal is a prime ideal as well as the problem when such an ideal possesses a quadratic Gr\"obner basis is solved. Second, we describe explicitly a primary…