# CLIFFORD MODULES

@inproceedings{A1964CLIFFORDM, title={CLIFFORD MODULES}, author={A.}, year={1964} }

The purpose of the paper is to undertake a detailed investigation of the role of Clifford algebras and spinors in the K&theory of real vector bundles. On the one hand the use of Clifford algebras throws considerable light on the periodicity theorem for the stable orthogonal group. On the other hand the use of spinors seems essential in some of the finer points of the KO-theory which centre round the Thorn isomorphism. As far as possible we have endeavoured to make this paper self-contained…

## 382 Citations

A proof of Bott periodicity via Clifford algebras

- Mathematics
- 2009

The purpose of this note is to present a proof of the Bott periodicity theorem that is based on the periodicity of Clifford algebras. Such a proof was first predicted in [2], and then constructed in…

Clifford Algebras and Bott Periodicity

- Mathematics
- 2018

In [2], Atiyah, Bott and Shapiro calculated certain groups Ak associated to real Clifford algebra representations, and observed that they were isomorphic to KO−k(∗). The same can be said for complex…

Clifford module invariants of spin bundles

- Mathematics
- 1982

In this paper, we study KO-theory invariants of Spin bundles obtained by the a-construction from Clifford module representations of the Spinor group. We begin by describing their elementary…

Clifford Modules and Twisted K-Theory

- Mathematics
- 2008

Abstract.The purpose of this short paper is to make the link between the fundamental work of Atiyah, Bott and Shapiro [ABS] and twisted K-theory [DK] [R] [K5]. This link was implicit for a long time…

OP2 bundles in M-theory

- Mathematics
- 2008

Ramond has observed that the massless multiplet of eleven-dimensional supergravity can be generated from the decomposition of certain representation of the exceptional Lie group F4 into those of its…

Loop groups and twisted K-theory III

- Mathematics
- 2011

In this paper, we identify the Ad-equivariant twisted K-theory of a compact Lie group G with the “Verlinde group” of isomorphism classes of admissible representations of its loop groups. Our…

Clifford modules and invariants of quadratic forms

- Mathematics
- 2010

Let A be a commutative ring with 1/2 in A. In this paper, we define new characteristic classes for finitely generated projective A-modules V provided with a non degenerate quadratic form. These…

RealCliffordAlgebras and Quadratic Forms over F 2 : Two Old Problems Become One

- Mathematics
- 2016

C lifford algebras are important for many areas of pure and applied mathematics and physics. Real Clifford algebras were introduced by the English mathematician and philosopher William Kingdon…

Clifford Periodicity from Finite Groups February 7 , 2008

- Mathematics
- 2008

We deduce the periodicity 8 for the type of Pin and Spin representations of the orthogonal groups O(n) from simple combinatorial properties of the finite Clifford groups generated by the gamma…

Real K-theories

- Mathematics
- 2020

The purpose of this short paper is to investigate relations between various real K-theories. In particular, we show how a real projective bundle theorem implies an unexpected relation between…

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