scholarly journals Rational extensions of the representation ring global functor and a splitting of global equivariant K-theory

2018 ◽  
Vol 50 (5) ◽  
pp. 863-873
Author(s):  
Christian Wimmer
Keyword(s):  
Representation Ring ◽  
K Theory

scholarly journals Symmetries of Kirchberg Algebras

2003 ◽  
Vol 46 (4) ◽  
pp. 509-528 ◽  
Author(s):  
David J. Benson ◽  
Alex Kumjian ◽  
N. Christopher Phillips
Keyword(s):  
Abelian Groups ◽  
Finitely Generated ◽  
Nontrivial Element ◽  
Direct Sum ◽  
Representation Ring ◽  
Direct Sum Decomposition ◽  
K Theory ◽  
Universal Coefficient Theorem ◽  
The Way

AbstractLet G0 and G1 be countable abelian groups. Let γi be an automorphism of Gi of order two. Then there exists a unital Kirchberg algebra A satisfying the Universal Coefficient Theorem and with [1A] = 0 in K0(A), and an automorphism α ∈ Aut(A) of order two, such that K0(A) ≅ G0, such that K1(A) ≅ G1, and such that α* : Ki(A) → Ki(A) is γi. As a consequence, we prove that every -graded countable module over the representation ring R() of is isomorphic to the equivariant K-theory K (A) for some action of on a unital Kirchberg algebra A.Along the way, we prove that every not necessarily finitely generated []-module which is free as a -module has a direct sum decomposition with only three kinds of summands, namely [] itself and on which the nontrivial element of acts either trivially or by multiplication by −1.

scholarly journals The Bott cofiber sequence in deformation K-theory and simultaneous similarity in U(n)

2009 ◽  
Vol 146 (2) ◽  
pp. 379-393 ◽  
Author(s):  
TYLER LAWSON
Keyword(s):  
Unitary Matrices ◽  
Bott Periodicity ◽  
Representation Ring ◽  
K Theory

AbstractWe show that there is a homotopy cofiber sequence of spectra relating Carlsson's deformation K-theory of a group G to its “deformation representation ring,” analogous to the Bott periodicity sequence relating connective K-theory to ordinary homology. We then apply this to study simultaneous similarity of unitary matrices.

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
Sign in / Sign up

Export Citation Format

Share Document