scholarly journals A Hilbert bundle description of differential K-theory

2018 ◽  
Vol 328 ◽  
pp. 661-712 ◽  
Author(s):  
Alexander Gorokhovsky ◽  
John Lott
Keyword(s):  
Hilbert Bundle ◽  
K Theory

scholarly journals 3D Current Algebra and Twisted K Theory

2018 ◽  
Vol 30 (07) ◽  
pp. 1840011
Author(s):  
Jouko Mickelsson
Keyword(s):  
Current Algebra ◽  
Fock Space ◽  
Abelian Extension ◽  
Fredholm Operators ◽  
Gauge Transformations ◽  
Infinite Dimensional ◽  
Loop Algebras ◽  
Hilbert Space Operators ◽  
Hilbert Bundle ◽  
K Theory

Equivariant twisted K theory classes on compact Lie groups [Formula: see text] can be realized as families of Fredholm operators acting in a tensor product of a fermionic Fock space and a representation space of a central extension of the loop algebra [Formula: see text] using a supersymmetric Wess–Zumino–Witten model. The aim of the present paper is to extend the construction to higher loop algebras using an abelian extension of a 3D current algebra. We have only partial success: Instead of true Fredholm operators we have formal algebraic expressions in terms of the generators of the current algebra and an infinite dimensional Clifford algebra. These give rise to sesquilinear forms in a Hilbert bundle which transform in the expected way with respect to 3D gauge transformations but do not define true Hilbert space operators.

An Introduction to K-Theory for C*-Algebras

2000 ◽  
Author(s):  
M. Rørdam ◽  
F. Larsen ◽  
N. Laustsen
Keyword(s):  
C Algebras ◽  
K Theory

On a question of swan in algebraic k-theory

1973 ◽  
Vol 6 (1) ◽  
pp. 85-94 ◽  
Author(s):  
Pramod K. Sharma ◽  
Jan R. Strooker
Keyword(s):  
K Theory

scholarly journals Wilson loop algebras and quantum K-theory for Grassmannians

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Hans Jockers ◽  
Peter Mayr ◽  
Urmi Ninad ◽  
Alexander Tabler
Keyword(s):  
Wilson Loop ◽  
Gauge Theories ◽  
Wilson Line ◽  
Quantum Cohomology ◽  
Three Dimensional ◽  
Loop Algebra ◽  
Loop Algebras ◽  
Verlinde Algebra ◽  
K Theory ◽  
Chern Simons

Abstract We study the algebra of Wilson line operators in three-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric U(M ) gauge theories with a Higgs phase related to a complex Grassmannian Gr(M, N ), and its connection to K-theoretic Gromov-Witten invariants for Gr(M, N ). For different Chern-Simons levels, the Wilson loop algebra realizes either the quantum cohomology of Gr(M, N ), isomorphic to the Verlinde algebra for U(M ), or the quantum K-theoretic ring of Schubert structure sheaves studied by mathematicians, or closely related algebras.

scholarly journals Toward AGT for Parabolic Sheaves

2020 ◽  
Author(s):  
Andrei Neguţ
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Conformal Field Theory ◽  
Moduli Spaces ◽  
Type A ◽  
Conformal Field ◽  
Toroidal Algebra ◽  
Agt Correspondence ◽  
K Theory ◽  
The Ideal

Abstract We construct explicit elements $W_{ij}^k$ in (a completion of) the shifted quantum toroidal algebra of type $A$ and show that these elements act by 0 on the $K$-theory of moduli spaces of parabolic sheaves. We expect that the quotient of the shifted quantum toroidal algebra by the ideal generated by the elements $W_{ij}^k$ will be related to $q$-deformed $W$-algebras of type $A$ for arbitrary nilpotent, which would imply a $q$-deformed version of the Alday-Gaiotto-Tachikawa (AGT) correspondence between gauge theory with surface operators and conformal field theory.

scholarly journals Graded K-theory and K-homology of relative Cuntz–Pimsner algebras and graph C⁎-algebras

2021 ◽  
Vol 496 (2) ◽  
pp. 124822
Author(s):  
Quinn Patterson ◽  
Adam Sierakowski ◽  
Aidan Sims ◽  
Jonathan Taylor
Keyword(s):  
C Algebras ◽  
K Theory

scholarly journals Eigenvalues, K-theory and Minimal Flows

2007 ◽  
Vol 59 (3) ◽  
pp. 596-613 ◽  
Author(s):  
Benjamín A. Itzá-Ortiz
Keyword(s):  
Dynamical System ◽  
Suspension Flow ◽  
Order Isomorphism ◽  
K Theory

AbstractLet (Y, T) be a minimal suspension flow built over a dynamical system (X, S) and with (strictly positive, continuous) ceiling function f : X → ℝ. We show that the eigenvalues of (Y, T) are contained in the range of a trace on the K0-group of (X, S). Moreover, a trace gives an order isomorphism of a subgroup of K0(C(X) ⋊Sℤ) with the group of eigenvalues of (Y, T). Using this result, we relate the values of t for which the time-t map on the minimal suspension flow is minimal with the K-theory of the base of this suspension.

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