Erratum to: K-Theory

Karoubi, Max

doi:10.1007/978-3-540-79890-3_6

Cited by 101 publications

(242 citation statements)

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“…In this somewhat extensive appendix, we present a summary of some basic notions of K-theory (and its connection to string theory), as well as technical details of various K-theory calculations needed for some of our arguments in the body of the paper. For a more comprehensive introduction to K-theory, the reader should consult [21,23,22,24]. Some elementary K-theory facts that arise in the string theory context can also be found in [2,3].…”

Section: Appendix a Useful Facts In K-theorymentioning

confidence: 99%

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Brane transfer operations and T-duality of non-BPS states

Bergman

Gimon

Hořava

1999

J. High Energy Phys.

145

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Using the relation between D-brane charges and K-theory, we study non-BPS D-branes and their behavior under T-duality. We point out that in general compactifications, D-brane charges are classified by relative K-theory groups. T-duality is found to act as a symmetry between the relative K-theory groups in Type II and Type I/IA theories. We also study Type IA theory (which contains an O8 − plane and an O8 + plane), using K-theory and T-duality to identify its stable D-branes. Comparison with string theory constructions reveals two interesting effects. One of them involves the transfer of branes between Oplanes, while in the other, a D-brane charge which seems conserved near one O-plane in fact decays due to the presence of another type of O-plane.

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Section: Appendix a Useful Facts In K-theorymentioning

confidence: 99%

“…There is an alternative definition of K −1 (X), in terms of pairs (E, α) where E is a bundle on X and α is an automorphism on E (see, e.g., [21], II.3.3). It is, in fact, this…”

Section: Appendix a Useful Facts In K-theorymentioning

confidence: 99%

Brane transfer operations and T-duality of non-BPS states

Bergman

Gimon

Hořava

1999

J. High Energy Phys.

145

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“…Atiyah et al [57] is the classic reference on modules over Clifford algebras; see also [58,59]. The following theorems tell us that (~, n, Q), Chevalley goes on to discuss the orthogonal group of (~, n, Q).…”

Section: The Clifford Algebra Of a Vector Spacementioning

confidence: 99%

“…An excellent exposition is given in the book by Karoubi [58]. An excellent exposition is given in the book by Karoubi [58].…”

Section: The Clifford Algebra Of a Vector Spacementioning

confidence: 99%

The Clifford algebra of differential forms

Salingaros

Wene

1985

Acta Appl Math

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This paper reviews Clifford algebras in mathematics and in theoretical physics. In particular, the little-known differential form realization is constructed in detail for the four-dimensional Minkowski space. This setting is then used to describe spinors as differential forms, and to solve the Klein-Gordon and Kahler-Dirac equations. The approach of this paper, in obtaining the solutions directly in terms of differential forms, is much more elegant and concise than the traditional explicit matrix methods. A theorem given here differentiates between the two real forms of the Dirac algebra by showing that spin can be accommodated in only one of them. (1980). 15A66, 15A75, 15A90, 53A50, 58A10, 81C05. AMS (MOS) subject classifications

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“…See also[2,7,13,14,25] for further details on this approach to the Bott periodicity theorem, at least for the K-theory of C Ã -algebras.…”

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confidence: 99%