Dimension and enumeration of primitive ideals in quantum algebras
نویسندگان
چکیده
In this paper, we study the primitive ideals of quantum algebras supporting a rational torus action. We first prove a quantum analogue of a Theorem of Dixmier; namely, we show that the Gelfand-Kirillov dimension of primitive factors of various quantum algebras is always even. Next we give a combinatorial criterion for a prime ideal that is invariant under the torus action to be primitive. We use this criterion to obtain a formula for the number of primitive ideals in the algebra of 2 × n quantum matrices that are invariant under the action of the torus. Roughly speaking, this can be thought of as giving an enumeration of the points that are invariant under the induced action of the torus in the “variety of 2 × n quantum matrices”.
منابع مشابه
Primitive Ideal Space of Ultragraph $C^*$-algebras
In this paper, we describe the primitive ideal space of the $C^*$-algebra $C^*(mathcal G)$ associated to the ultragraph $mathcal{G}$. We investigate the structure of the closed ideals of the quotient ultragraph $ C^* $-algebra $C^*left(mathcal G/(H,S)right)$ which contain no nonzero set projections and then we characterize all non gauge-invariant primitive ideals. Our results generalize the ...
متن کاملTitles and Abstracts for the Algebra Extravaganza
Title: The Dixmier-Moeglin equivalence for D-groups Abstract: The Dixmier-Moeglin equivalence is a characterization of the primitive ideals of an algebra that holds for many classes of rings, including affine PI rings, enveloping algebras of finite-dimensional Lie algebras, and many quantum algebras. For rings satisfying this equivalence, it says that the primitive ideals are precisely those pr...
متن کاملAdjacency metric dimension of the 2-absorbing ideals graph
Let Γ=(V,E) be a graph and W_(a)={w_1,…,w_k } be a subset of the vertices of Γ and v be a vertex of it. The k-vector r_2 (v∣ W_a)=(a_Γ (v,w_1),… ,a_Γ (v,w_k)) is the adjacency representation of v with respect to W in which a_Γ (v,w_i )=min{2,d_Γ (v,w_i )} and d_Γ (v,w_i ) is the distance between v and w_i in Γ. W_a is called as an adjacency resolving set for Γ if distinct vertices of ...
متن کاملThe Prime and Primitive Spectra of Multiparameter Quantum Symplectic and Euclidean Spaces
We investigate a class of algebras that provides multiparameter versions of both quantum symplectic space and quantum Euclidean 2n-space. These algebras encompass the graded quantized Weyl algebras, the quantized Heisenberg space, and a class of algebras introduced by Oh. We describe the structure of the prime and primitive ideals of these algebras. Other structural results include normal separ...
متن کاملPoisson Algebras via Model Theory and Differential-algebraic Geometry
Brown and Gordon asked whether the Poisson Dixmier-Moeglin equivalence holds for any complex affine Poisson algebra; that is, whether the sets of Poisson rational ideals, Poisson primitive ideals, and Poisson locally closed ideals coincide. In this article a complete answer is given to this question using techniques from differential-algebraic geometry and model theory. In particular, it is sho...
متن کامل