A quantum homogeneous space of nilpotent matrices
نویسنده
چکیده
A quantum deformation of the adjoint action of the special linear group on the variety of nilpotent matrices is introduced. New non-embedded quantum homogeneous spaces are obtained related to certain maximal coadjoint orbits, and known quantum homogeneous spaces are revisited. MSC: 16W35; 20G42; 17B37; 81R50
منابع مشابه
Products of commuting nilpotent operators
Matrices that are products of two (or more) commuting square-zero matrices and matrices that are products of two commuting nilpotent matrices are characterized. Also given are characterizations of operators on an infinite dimensional Hilbert space that are products of two (or more) commuting square-zero operators, as well as operators on an infinite-dimensional vector space that are products of...
متن کاملGeometrical Description of the Local Integrals of Motion of Maxwell-bloch Equation
We represent a classical Maxwell-Bloch equation and related to it positive part of the AKNS hierarchy in geometrical terms. The Maxwell-Bloch evolution is given by an infinitesimal action of a nilpotent subalgebra n+ of affine Lie algebra ŝl2 on a Maxwell-Bloch phase space treated as a homogeneous space of n+. A space of local integrals of motion is described using cohomology methods. We show t...
متن کاملUnipotent and Nakayama automorphisms of quantum nilpotent algebras
Automorphisms of algebras R from a very large axiomatic class of quantum nilpotent algebras are studied using techniques from noncommutative unique factorization domains and quantum cluster algebras. First, the Nakayama automorphism of R (associated to its structure as a twisted Calabi-Yau algebra) is determined and shown to be given by conjugation by a normal element, namely, the product of th...
متن کاملOn the nil-clean matrix over a UFD
In this paper we characterize all $2times 2$ idempotent and nilpotent matrices over an integral domain and then we characterize all $2times 2$ strongly nil-clean matrices over a PID. Also, we determine when a $2times 2$ matrix over a UFD is nil-clean.
متن کاملThe witness set of coexistence of quantum effects and its preservers
One of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. In this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. We also devote to characterizing bijective morphisms on quantum effects leaving the witness...
متن کامل