The notion of initial ideal for an a polynomial ring appears in the theory Gröbner basis. Similarly to ideals, we can define algebra subalgebra ring, or more generally Laurent which is used SAGBI (Subalgebra Analogue Bases Ideals) finitely generated not always generated, and no general criterion finite generation known. aim this paper present new class subalgebras having non-finitely algebras. ...

In this paper, we begin to study the subalgebra lattice of a Leibniz algebra. particular, deal with algebras whose is modular, upper semi-modular, lower distributive, or dually atomistic. The fact that non-Lie algebra has fewer one-dimensional subalgebras in general results number conditions being weaker than Lie case.

A Poisson geometry arising from maximal commutative subalgebras is studied. A spectral sequence convergent to Hochschild homology with coefficients in a bimodule is presented. It depends on the choice of a maximal commutative subalgebra inducing appropriate filtrations. Its E p,q -groups are computed in terms of canonical homology with values in a Poisson module defined by a given bimodule and ...

We introduce a new notion of a sufficient subalgebra for quantum states: a subalgebra is 2sufficient for a pair of states {ρ0, ρ1} if it contains all Bayes optimal tests of ρ0 against ρ1. In classical statistics, this corresponds to the usual definition of sufficiency. We show this correspondence in the quantum setting for some special cases. Furthermore, we show that sufficiency is equivalent ...

Abstract. In this paper we introduce doubly symmetric functions, arising from the equivalence of particular linear combinations of Schur functions and hook Schur functions. We study algebraic and combinatorial aspects of doubly symmetric functions, in particular as they form a subalgebra of the algebra of symmetric functions. This subalgebra is generated by the odd power sum symmetric functions...