English
Related papers

Related papers: Clifford modules and twisted K-theory

200 papers

Clifford theory relates the representation theory of finite groups to those of a fixed normal subgroup by means of induction and restriction, which is an adjoint pair of functors. We generalize this result to the situation of a…

Representation Theory · Mathematics 2023-01-27 Alexander Zimmermann

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

We construct power operations for twisted KR-theory of topological stacks. Standard algebraic properties of Clifford algebras imply that these power operations preserve universal Thom classes. As a consequence, we show that the twisted…

Algebraic Topology · Mathematics 2024-07-19 Daniel Berwick-Evans , Meng Guo

We compare different algebraic structures in twisted equivariant K-Theory for proper actions of discrete groups. After the construction of a module structure over untwisted equivariant K-Theory, we prove a completion Theorem of Atiyah-Segal…

K-Theory and Homology · Mathematics 2019-01-15 Noe Barcenas , Mario Velasquez

Clifford theory of possibly infinite dimensional modules is studied

Representation Theory · Mathematics 2015-12-31 Fernando Szechtman

The main goal of the present paper is the construction of twisted generalized differential cohomology theories and the comprehensive statement of its basic functorial properties. Technically it combines the homotopy theoretic approach to…

Algebraic Topology · Mathematics 2019-08-21 Ulrich Bunke , Thomas Nikolaus

Classical Clifford theory studies the decomposition of simple $G$-modules into simple $H$-modules for some normal subgroup $H \triangleleft G$. In this paper we deal with chains of normal subgroups $1 \triangleleft G_1 \triangleleft \cdots…

Representation Theory · Mathematics 2017-06-13 Frederik Caenepeel , Fred Van Oystaeyen

Expository notes on Clifford algebras and spinors with a detailed discussion of Majorana, Weyl, and Dirac spinors. The paper is meant as a review of background material, needed, in particular, in now fashionable theoretical speculations on…

Mathematical Physics · Physics 2011-10-28 Ivan Todorov

This is an expository account of the following result: we can construct a group by means of twisted Z_2-graded vectorial bundles which is isomorphic to K-theory twisted by any degree three integral cohomology class.

K-Theory and Homology · Mathematics 2008-03-08 Kiyonori Gomi

This work is devoted to the study of the foundations of quantum K-theory, a K-theoretic version of quantum cohomology theory. In particular, it gives a deformation of the ordinary K-ring K(X) of a smooth projective variety X, analogous to…

Algebraic Geometry · Mathematics 2022-01-12 Y. -P. Lee

We summarize the main results of our recent investigation of bundles of real Clifford modules and briefly touch on some applications to string theory and supergravity.

High Energy Physics - Theory · Physics 2020-08-04 C. I. Lazaroiu , C. S. Shahbazi

We study the relationship between the twisted Orbifold K-theories ${^{\alpha}}K_{orb}(\textsl{X})$ and ${^{\alpha'}}K_{orb}(\textsl{Y})$ for two different twists $\alpha\in Z^3(G;S^1)$ and $\alpha'\in Z^3(G';S^1)$ of the Orbifolds…

Algebraic Topology · Mathematics 2016-01-20 Edward Becerra , Hermes Martinez , Mario Velasquez

This paper is an elaboration of an introductory talk given by the author at a workshop on Clifford algebras at Tennessee Technical University, in May 2002. We give an introduction to the basic concepts of Clifford analysis, including links…

Complex Variables · Mathematics 2007-05-23 John Ryan

Given a field $K$ and an ample (not necessarily Hausdorff) groupoid $G$, we define the concept of a line bundle over $G$ inspired by the well known concept from the theory of C*-algebras. If $E$ is such a line bundle, we construct the…

Operator Algebras · Mathematics 2025-06-12 M. Dokuchaev , R. Exel , H. Pinedo

In this paper we show how to describe the general theory of a linear metric compatible connection with the theory of Clifford valued differential forms. This is done by realizing that for each spacetime point the algebra of Clifford…

Mathematical Physics · Physics 2007-05-23 E. Capelas de Oliveira , W. A. Rodrigues

We investigate the construction and properties of Clifford algebras by a similar manner as our previous construction of the octonions, namely as a twisting of group algebras of Z_2^n by a cocycle. Our approach is more general than the usual…

Quantum Algebra · Mathematics 2007-05-23 H. Albuquerque , S. Majid

Let X be a smooth irreducible projective surface. The aim of this paper is to establish a version of Clifford's theorem for coherent systems on X.

Algebraic Geometry · Mathematics 2024-08-02 L. Costa , I. Macías Tarrío , L. Roa-Leguizamón

Albuquerque and Majid have shown how to view Clifford algebras $\cl_{p,q}$ as twisted group rings whereas Chernov has observed that Clifford algebras can be viewed as images of group algebras of certain 2-groups modulo an ideal generated by…

Rings and Algebras · Mathematics 2016-10-13 Rafal Ablamowicz

This paper sets out basic properties of motivic twisted K-theory with respect to degree three motivic cohomology classes of weight one. Motivic twisted K-theory is defined in terms of such motivic cohomology classes by taking pullbacks…

Algebraic Topology · Mathematics 2010-08-31 Markus Spitzweck , Paul Arne Østvær

We establish the Thom isomorphism in twisted K-theory for any real vector bundle and develop the push-forward map in twisted K-theory for any differentiable proper map $f: X\to Y$ (not necessarily K-oriented). The push-forward map…

K-Theory and Homology · Mathematics 2007-05-23 Alan L. Carey , Bai-Ling Wang