On the quasi-exponent of finite-dimensional Hopf algebras [PDF]
, 2001 Recall (math.QA/9812151) that the exponent of a finite-dimensional complex Hopf algebra H is the order of the Drinfeld element u of the Drinfeld double D(H) of H. Recall also that while this order may be infinite, the eigenvalues of u are always roots of
P. Etingof, Shlomo Gelaki
semanticscholar +1 more source
, 1999 Recall that a finite group is called perfect if it does not have non-trivial 1-dimensional representations (over the field of complex numbers C). By analogy, let us say that a finite dimensional Hopf algebra H over C is perfect if any 1-dimensional H ...
P. Etingof +3 more
semanticscholar +1 more source
Improved Resource‐Tunable Near‐Term Quantum Algorithms for Transition Probabilities, with Applications in Physics and Variational Quantum Linear Algebra [PDF]
Advanced Quantum Technologies, 2022 Transition amplitudes and transition probabilities are relevant to many areas of physics simulation, including the calculation of response properties and correlation functions.
Nicolas P. D. Sawaya, J. Huh
semanticscholar +1 more source
A simple algebraic proof of the algebraic index theorem [PDF]
, 2004 In math.QA/0311303 B. Feigin, G. Felder, and B. Shoikhet proposed an explicit formula for the trace density map from the quantum algebra of functions on an arbitrary symplectic manifold M to the top degree cohomology of M. They also evaluated this map on
Po-Ning Chen, V. Dolgushev
semanticscholar +1 more source
Statistics of projective measurement on a quantum probe as a witness of noncommutativity of algebra of a probed system [PDF]
Quantum Information Processing, 2021 We consider a quantum probe P undergoing pure dephasing due to its interaction with a quantum system S. The dynamics of P is then described by a well-defined sub-algebra of operators of S, i.e.
Fattah Sakuldee, Ł. Cywiński
semanticscholar +1 more source
RosneT: A Block Tensor Algebra Library for Out-of-Core Quantum Computing Simulation [PDF]
2021 IEEE/ACM Second International Workshop on Quantum Computing Software (QCS), 2021 With the advent of more powerful Quantum Computers, the need for larger Quantum Simulations has boosted. As the amount of resources grows exponentially with size of the target system Tensor Networks emerge as an optimal framework with which we represent ...
Sergio Sánchez Ramírez +6 more
semanticscholar +1 more source
Classification of quantum groups and Belavin--Drinfeld cohomologies for orthogonal and symplectic Lie algebras [PDF]
, 2015 In this paper we continue to study Belavin-Drinfeld cohomology introduced in arXiv:1303.4046 [math.QA] and related to the classification of quantum groups whose quasi-classical limit is a given simple complex Lie algebra. Here we compute Belavin-Drinfeld
Alexander Stolin +6 more
core +2 more sources
Twenty-five years of two-dimensional rational conformal field theory [PDF]
, 2009 In this article we try to give a condensed panoramic view of the development of two-dimensional rational conformal field theory in the last twenty-five years.Comment: A review for the 50th anniversary of the Journal of Mathematical Physics.
Axelrod S. +37 more
core +1 more source
The Universal Askey-Wilson Algebra [PDF]
, 2011 In 1992 A. Zhedanov introduced the Askey-Wilson algebra AW=AW(3) and used it to describe the Askey-Wilson polynomials. In this paper we introduce a central extension $\Delta$ of AW, obtained from AW by reinterpreting certain parameters as central ...
Terwilliger, Paul
core +3 more sources
Quantum Isometry Group for Spectral Triples with Real Structure [PDF]
, 2010 Given a spectral triple of compact type with a real structure in the sense of [Dabrowski L., J. Geom. Phys. 56 (2006), 86-107] (which is a modification of Connes' original definition to accommodate examples coming from quantum group theory) and ...
Goswami, Debashish
core +6 more sources