scholarly journals K-theory of Hermitian Mackey functors, real traces, and assembly

2019 ◽  
Vol 4 (2) ◽  
pp. 243-316
Author(s):  
Emanuele Dotto ◽  
Crichton Ogle
Keyword(s):  
Mackey Functors ◽  
K Theory

scholarly journals Spectral Mackey functors and equivariant algebraic K-theory, II

2020 ◽  
Vol 2 (1) ◽  
pp. 97-146 ◽  
Author(s):  
Clark Barwick ◽  
Saul Glasman ◽  
Jay Shah
Keyword(s):  
Mackey Functors ◽  
K Theory

The slice spectral sequence for the C4$C_{4}$ analog of real K-theory

2017 ◽  
Vol 29 (2) ◽  
pp. 383-447 ◽  
Author(s):  
Michael A. Hill ◽  
Michael J. Hopkins ◽  
Douglas C. Ravenel
Keyword(s):  
Spectral Sequence ◽  
The Real ◽  
Mackey Functor ◽  
Partial Analysis ◽  
Mackey Functors ◽  
K Theory

AbstractWe describe the slice spectral sequence of a 32-periodic $C_{4}$-spectrum $K_{[2]}$ related to the $C_{4}$ norm ${\mathrm{MU}^{((C_{4}))}=N_{C_{2}}^{C_{4}}\mathrm{MU}_{\mathbb{R}}}$ of the real cobordism spectrum $\mathrm{MU}_{\mathbb{R}}$. We will give it as a spectral sequence of Mackey functors converging to the graded Mackey functor $\underline{\pi}_{*}K_{[2]}$, complete with differentials and exotic extensions in the Mackey functor structure. The slice spectral sequence for the 8-periodic real K-theory spectrum $K_{\mathbb{R}}$ was first analyzed by Dugger. The $C_{8}$ analog of $K_{[2]}$ is 256-periodic and detects the Kervaire invariant classes $\theta_{j}$. A partial analysis of its slice spectral sequence led to the solution to the Kervaire invariant problem, namely the theorem that $\theta_{j}$ does not exist for ${j\geq 7}$.

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.

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