相关论文: Quantized trace rings

Let G be a subgroup of finite index in SL(n,Z) for N > 4. Suppose G acts continuously on a manifold M, with fundamental group Z^n, preserving a measure that is positive on open sets. Further assume that the induced G action on H^1(M) is…

The question of general covariance in quantum gravity is considered in the first post-Newtonian approximation. Transformation properties of observable quantities under deformations of a reference frame, induced by variations of the gauge…

We construct a class of positive linear maps on matrix algebras. We find conditions when these maps are atomic, decomposable and completely positive. We obtain a large class of atomic positive linear maps. As applications in quantum…

We examine a few problems of enumerative geometry and present their solutions in the framework of deformed (quantum) cohomology rings.

We study the quantum groups appearing via models $C(G)\subset M_K(C(X))$ which are "stationary", in the sense that the Haar integration over $G$ is the functional $tr\otimes\int_X$. Our results include a number of generalities, notably with…

We construct twisting elements for module algebras of restricted two-parameter quantum groups from factors of their R-matrices. We generalize the theory of Giaquinto and Zhang to universal deformation formulas for categories of module…

Given a linear action of a group $G$ on a $K$-vector space $V$, we consider the invariant ring $K[V \oplus V^*]^G$, where $V^*$ is the dual space. We are particularly interested in the case where $V =\gfq^n$ and $G$ is the group $U_n$ of…

Sequences of commuting quantum operators can be parallelized using entanglement. This transformation is behind some optimal quantum metrology protocols and recent results on quantum circuit complexity. We show that dephasing quantum maps in…

We present a novel, universal description of quantum entanglement using group theory and generalized characteristic functions. It leads to new reformulations of the separability problem, and the positivity of partial transpose (PPT)…

We formulate three current models of discrete-time quantum walks in a combinatorial way. These walks are shown to be closely related to rotation systems and 1-factorizations of graphs. For two of the models, we compute the traces and total…

The q-deformed traces and orbits for the two parametric quantum groups $GL_{qp}(2)$ and $GL_{qp}(1|1)$ are defined. They are subsequently used in the construction of $q$-orbit invariants for these groups. General $qp$-(super)oscillator…

We extend Latimer and MacDuffee's theorem to a general commutative domain and apply this result to study similarity of matrices over integral rings of number fields. We also conjecture similarity over discrete valuation rings can be descent…

General algebraic properties of the algebras of vector fields over quantum linear groups $GL_q(N)$ and $SL_q(N)$ are studied. These quantum algebras appears to be quite similar to the classical matrix algebra. In particular, quantum…

The theory of generalized inverses of matrices and operators is closely connected with projections, i.e., idempotent (bounded) linear transformations. We show that a similar situation occurs in any associative ring $\mathcal{R}$ with a unit…

The general linear group GL(n) acts on the direct sum of $m$ copies of Mat(n) by the adjoint action. The action of GL(n) induces the action of the unitriangular subgroup U. We present the system of free generators of the field of…

In this paper, we study the ring of invariants under the action of SL(m,K)\times SL(n,K) and SL(m,K)\times SL(n,K)\times SL(2,K) on the 3-dimensional array of indeterminates of form m\times n\times 2, where K is an infinite field. And we…

In this article, we study the multi-parameter quantum groups defined by generators and relations associated with symmetrizable generalized Cartan matrices, together with their representations in the category $\mathcal O$. This presentation…

We study quantum walks on general graphs from the point of view of scattering theory. For a general finite graph we choose two vertices and attach one half line to each. We are interested in walks that proceed from one half line, through…

The trace on matrix rings, along with the augmentation map and Kaplansky trace on group rings, are some of the many examples of linear functions on algebras that vanish on all commutators. We generalize and unify these examples by studying…

Invariants of generalized tensor fields on a line are classified using special polynomials P_mk^(-1/lambda) introduced here for this purpose. For the case of positive characteristic, a new invariant of formal power series, a width, is…