scholarly journals Finite generation of some cohomology rings via twisted tensor product and Anick resolutions

2019 ◽  
Vol 223 (1) ◽  
pp. 316-339
Author(s):  
Van C. Nguyen ◽  
Xingting Wang ◽  
Sarah Witherspoon
Keyword(s):  
Tensor Product ◽  
Finite Generation ◽  
Cohomology Rings ◽  
Twisted Tensor Product

Cartan's constructions and the twisted Eilenberg–Zilber theorem

2010 ◽  
Vol 17 (1) ◽  
pp. 13-23
Author(s):  
Víctor Álvarez ◽  
José Andrés Armario ◽  
María Dolores Frau ◽  
Pedro Real
Keyword(s):  
Perturbation Theory ◽  
Tensor Product ◽  
Cartesian Product ◽  
Tensor Products ◽  
Standard Product ◽  
Homological Perturbation Theory ◽  
Twisted Tensor Product ◽  
Homological Perturbation ◽  
Twisted Cartesian Product

Abstract Let 𝐺 × τ 𝐺′ be the principal twisted Cartesian product with fibre 𝐺, base 𝐺 and twisting function where 𝐺 and 𝐺′ are simplicial groups as well as 𝐺 × τ 𝐺′; and 𝐶𝑁(𝐺) ⊗𝑡 𝐶𝑁 (𝐺′) be the twisted tensor product associated to 𝐶𝑁 (𝐺 × τ 𝐺′) by the twisted Eilenberg–Zilber theorem. Here we prove that the pair 𝐶𝑁(𝐺) ⊗𝑡 𝐶𝑁(𝐺′), μ) is a multiplicative Cartan's construction where μ is the standard product on 𝐶𝑁(𝐺) ⊗ 𝐶𝑁(𝐺′). Furthermore, assuming that a contraction from 𝐶𝑁(𝐺′) to 𝐻𝐺′ exists and using the techniques from homological perturbation theory, we extend the former result to other “twisted” tensor products of the form 𝐶𝑁(𝐺) ⊗ 𝐻𝐺′.

TWISTED TENSOR PRODUCT MODULES OVER MÖBIUS TWISTED TENSOR PRODUCT NONLOCAL VERTEX ALGEBRAS

2013 ◽  
Vol 24 (05) ◽  
pp. 1350033 ◽  
Author(s):  
JIANCAI SUN ◽  
HENGYUN YANG
Keyword(s):  
Tensor Product ◽  
Vertex Algebra ◽  
Vertex Algebras ◽  
The Third ◽  
Twisted Tensor Product

This is the third part in a series of papers developing a twisted tensor product theory for nonlocal vertex algebras and its modules. In this paper we introduce and study twisted tensor product modules over Möbius twisted tensor product nonlocal vertex algebras. Among the main results, we find the isomorphic relation between the opposite Möbius twisted tensor product nonlocal vertex algebra and twisted tensor product of opposite Möbius nonlocal vertex algebras. And we also establish the isomorphism between two twisted tensor product contragredient modules. Furthermore, we study iterated twisted tensor product modules over iterated twisted tensor product nonlocal vertex algebras and find conditions for constructing an iterated twisted tensor product module of three factors.

Finite generation of the cohomology rings for the extension algebras of monomial algebras

2022 ◽  
Author(s):  
Hongbo Shi
Keyword(s):  
Cohomology Ring ◽  
Minimal Resolution ◽  
Finitely Generated ◽  
Finite Generation ◽  
Cohomology Rings ◽  
Monomial Algebra ◽  
Monomial Algebras ◽  
Resolution Graph ◽  
Dual Extension

We describe the cohomology ring of a monomial algebra in the language of dimension tree or minimal resolution graph and in this context we study the finite generation of the cohomology rings of the extension algebras, showing among others that the cohomology ring [Formula: see text] is finitely generated [Formula: see text] is [Formula: see text] is, where [Formula: see text] is the dual extension of a monomial algebra [Formula: see text] and [Formula: see text] is the opposite algebra of [Formula: see text].

scholarly journals New approaches to finite generation of cohomology rings

2021 ◽  
Author(s):  
Van C. Nguyen ◽  
Xingting Wang ◽  
Sarah Witherspoon
Keyword(s):  
Finite Generation ◽  
Cohomology Rings ◽  
New Approaches

scholarly journals QUANTUM GROUP-TWISTED TENSOR PRODUCTS OF C*-ALGEBRAS

2014 ◽  
Vol 25 (02) ◽  
pp. 1450019 ◽  
Author(s):  
RALF MEYER ◽  
SUTANU ROY ◽  
STANISŁAW LECH WORONOWICZ
Keyword(s):  
Hilbert Space ◽  
Tensor Product ◽  
Quantum Group ◽  
Quantum Groups ◽  
Tensor Products ◽  
Group Representations ◽  
Basic Properties ◽  
C Algebras ◽  
Twisted Tensor Product

We put two C*-algebras together in a noncommutative tensor product using quantum group coactions on them and a bicharacter relating the two quantum groups that act. We describe this twisted tensor product in two equivalent ways, based on certain pairs of quantum group representations and based on covariant Hilbert space representations, respectively. We establish basic properties of the twisted tensor product and study some examples.

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