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Related papers: Relations in Twisted Quantum K-Rings

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We introduce a general framework to unify several variants of twisted topological $K$-theory. We focus on the role of finite dimensional real simple algebras with a product-preserving involution, showing that Grothendieck-Witt groups…

K-Theory and Homology · Mathematics 2015-09-29 Max Karoubi , Charles Weibel

We propose an approach via Frobenius manifolds to the study (began in math.AG/0407254) of the relation between rational Gromov-Witten invariants of nonabelian quotients X//G and those of the corresponding ``abelianized'' quotients X//T, for…

Algebraic Geometry · Mathematics 2011-01-04 Ionut Ciocan-Fontanine , Bumsig Kim , Claude Sabbah

Let $G$ be a split semisimple linear algebraic group over a field and let $X$ be a generic twisted flag variety of $G$. Extending the Hilbert basis techniques to Laurent polynomials over integers we give an explicit presentation of the…

Algebraic Geometry · Mathematics 2017-11-01 Sanghoon Baek , Rostislav Devyatov , Kirill Zainoulline

Recent work [hep-th/0504183,hep-th/0508002] indicates an approach to the formulation of diffeomorphism invariant quantum field theories (qft's) on the Groenewold-Moyal (GM) plane. In this approach to the qft's, statistics gets twisted and…

High Energy Physics - Theory · Physics 2008-11-26 A. P. Balachandran , A. Pinzul , B. A. Qureshi , S. Vaidya

The quantum Grothendieck ring of a certain category of finite-dimensional modules over a quantum loop algebra associated with a complex finite-dimensional simple Lie algebra $\mathfrak{g}$ has a quantum cluster algebra structure of…

Representation Theory · Mathematics 2023-10-11 Il-Seung Jang , Kyu-Hwan Lee , Se-jin Oh

In GT/0006019 oriented quantum algebras were motivated and introduced in a natural categorical setting. Invariants of knots and links can be computed from oriented quantum algebras, and this includes the Reshetikhin-Turaev theory for Ribbon…

Geometric Topology · Mathematics 2007-05-23 Louis H. Kauffman , David E. Radford

We describe a map from the equivariant twisted K-homology of a compact, connected, simply connected Lie group $G$ to the Verlinde ring. Our map is described at the level of `D-cycles' for the geometric twisted K-homology of $G$, and is…

K-Theory and Homology · Mathematics 2019-07-03 Yiannis Loizides

We offer here a more direct approach to twisted K-theory, based on the notion of twisted vector bundles (of finite or infinite dimension) and of twisted principal bundles. This is closeely related to the classical notion ot torsors and…

K-Theory and Homology · Mathematics 2010-12-14 Max Karoubi

We define twisted equivariant K-homology groups using geometric cycles. We compare them with approaches using Kasparov KK-Theory and (twisted) group C*-algebras.

K-Theory and Homology · Mathematics 2015-01-27 Noe Barcenas

We provide a systematic approach to describing the Ramond-Ramond (RR) fields as elements in twisted differential K-theory. This builds on a series of constructions by the authors on geometric and computational aspects of twisted…

High Energy Physics - Theory · Physics 2024-06-18 Daniel Grady , Hisham Sati

We investigate quantum communication between the sites of a spin-ring with twisted boundary conditions. Such boundary conditions can be achieved by a flux through the ring. We find that a non-zero twist can improve communication through…

Quantum Physics · Physics 2009-11-10 S. Bose , B. -Q. Jin , V. E. Korepin

This is the first in a series of papers constructing geometric models of twisted differential K-theory. In this paper we construct a model of even twisted differential K-theory when the underlying topological twist represents a torsion…

K-Theory and Homology · Mathematics 2020-03-18 Byungdo Park

We describe the quantum cohomology rings of a class of toric varieties. The description includes, in addition to the (already known) ring presentations, the (new) analogues for toric varieties of the sorts of quantum Giambelli formulas…

Algebraic Geometry · Mathematics 2007-05-23 Andrew Kresch

Higher twisted $K$-theory is an extension of twisted $K$-theory introduced by Ulrich Pennig which captures all of the homotopy-theoretic twists of topological $K$-theory in a geometric way. We give an overview of his formulation and key…

K-Theory and Homology · Mathematics 2020-07-20 David Brook

We study the Kawai-Lewellen-Tye (KLT) relations for quantum field theory by reformulating it as an isomorphism between two Lie algebras. We also show how explicit formulas for KLT relations arise when studying rational functions on…

High Energy Physics - Theory · Physics 2021-11-16 Hadleigh Frost

Twisted K-theory has its origins in the author's PhD thesis [27] : http://www.numdam.org/item?id=ASENS_1968_4_1_2_161_0 and in the paper with P. Donovan http://www.numdam.org/item?id=PMIHES_1970__38__5_0 The objective of this paper is to…

K-Theory and Homology · Mathematics 2007-08-23 Max Karoubi

$q$-Yangians can be viewed both as quantum deformations of the loop algebras of upper triangular Lie algebras and deformations of the Yangian algebras. In this paper, we study the quantum affine algebra as a product of two copies of the…

Quantum Algebra · Mathematics 2025-03-18 Naihuan Jing , Jian Zhang

Recently twisted K-theory has received much attention due to its applications in string theory and the announced result by Freed, Hopkins and Telemann relating the twisted equivariant K-theory of a compact Lie group to its Verlinde algebra.…

Differential Geometry · Mathematics 2007-05-23 Marco Mackaay

These are notes on twisted K-homology theory and twisted Ext-theory from the C*-algebra viewpoint, part of a series of talks on ``C*-algebras, noncommutative geometry and K-theory'', primarily for physicists.

High Energy Physics - Theory · Physics 2007-05-23 V. Mathai , I. M. Singer

We show how general principles of symmetry in quantum mechanics lead to twisted notions of a group representation. This framework generalizes both the classical 3-fold way of real/complex/quaternionic representations as well as a…

High Energy Physics - Theory · Physics 2015-06-11 Daniel S. Freed , Gregory W. Moore