scholarly journals The extension algebra of some cohomological Mackey functors

2015 ◽  
Vol 283 ◽  
pp. 51-87
Author(s):  
Serge Bouc ◽  
Radu Stancu
Keyword(s):  
Mackey Functors ◽  
Extension Algebra

scholarly journals Cyclic-Homology Chern–Weil Theory for Families of Principal Coactions

2020 ◽  
Author(s):  
Piotr M. Hajac ◽  
Tomasz Maszczyk
Keyword(s):  
Cyclic Homology ◽  
Quantum Deformation ◽  
Homotopy Formula ◽  
Standard Quantum ◽  
Unital Algebra ◽  
Hopf Fibrations ◽  
Chain Homotopy ◽  
Cartan Model ◽  
Extension Algebra ◽  
Hochschild Complex

AbstractViewing the space of cotraces in the structural coalgebra of a principal coaction as a noncommutative counterpart of the classical Cartan model, we construct the cyclic-homology Chern–Weil homomorphism. To realize the thus constructed Chern–Weil homomorphism as a Cartan model of the homomorphism tautologically induced by the classifying map on cohomology, we replace the unital subalgebra of coaction-invariants by its natural H-unital nilpotent extension (row extension). Although the row-extension algebra provides a drastically different model of the cyclic object, we prove that, for any row extension of any unital algebra over a commutative ring, the row-extension Hochschild complex and the usual Hochschild complex are chain homotopy equivalent. It is the discovery of an explicit homotopy formula that allows us to improve the homological quasi-isomorphism arguments of Loday and Wodzicki. We work with families of principal coactions, and instantiate our noncommutative Chern–Weil theory by computing the cotrace space and analyzing a dimension-drop-like effect in the spirit of Feng and Tsygan for the quantum-deformation family of the standard quantum Hopf fibrations.

scholarly journals Jordan centralizer maps on trivial extension algebras

2020 ◽  
Vol 53 (1) ◽  
pp. 58-66
Author(s):  
Mohammad Ali Bahmani ◽  
Fateme Ghomanjani ◽  
Stanford Shateyi
Keyword(s):  
Trivial Extension ◽  
Triangular Algebra ◽  
Trivial Extension Algebra ◽  
Extension Algebra

AbstractThe structure of Jordan centralizer maps is investigated on trivial extension algebras. One may obtain some conditions under which a Jordan centralizer map on a trivial extension algebra is a centralizer map. As an application, we characterize the Jordan centralizer map on a triangular algebra.

scholarly journals The Structure of Mackey Functors

1995 ◽  
Vol 347 (6) ◽  
pp. 1865 ◽  
Author(s):  
Jacques Thevenaz ◽  
Peter Webb
Keyword(s):  
Mackey Functors

scholarly journals EXTENSION ALGEBRAS OF CUNTZ ALGEBRA, II

2009 ◽  
Vol 80 (1) ◽  
pp. 83-90 ◽  
Author(s):  
SHUDONG LIU ◽  
XIAOCHUN FANG
Keyword(s):  
Hilbert Space ◽  
Compact Operators ◽  
Cuntz Algebra ◽  
Infinite Dimensional ◽  
Algebra Ii ◽  
Infinite Dimensional Hilbert Space ◽  
Dimensional Hilbert Space ◽  
K Theory ◽  
Extension Algebra

AbstractIn this paper, we construct the unique (up to isomorphism) extension algebra, denoted by E∞, of the Cuntz algebra 𝒪∞ by the C*-algebra of compact operators on a separable infinite-dimensional Hilbert space. We prove that two unital monomorphisms from E∞ to a unital purely infinite simple C*-algebra are approximately unitarily equivalent if and only if they induce the same homomorphisms in K-theory.

scholarly journals Mackey Functors with Chain Conditions

1998 ◽  
Vol 205 (2) ◽  
pp. 661-698
Author(s):  
Florian Luca
Keyword(s):  
Chain Conditions ◽  
Mackey Functors
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