scholarly journals Hochschild cohomology of twisted tensor products

2022 ◽  
Author(s):  
Benjamin Briggs ◽  
Sarah Witherspoon
Keyword(s):  
Hochschild Cohomology ◽  
Tensor Products

scholarly journals Gerstenhaber brackets on Hochschild cohomology of twisted tensor products

2017 ◽  
Vol 11 (4) ◽  
pp. 1351-1379 ◽  
Author(s):  
Lauren Grimley ◽  
Van Nguyen ◽  
Sarah Witherspoon
Keyword(s):  
Hochschild Cohomology ◽  
Tensor Products

scholarly journals Gerstenhaber brackets on Hochschild cohomology of general twisted tensor products

2021 ◽  
Vol 225 (6) ◽  
pp. 106597
Author(s):  
Tekin Karadağ ◽  
Dustin McPhate ◽  
Pablo S. Ocal ◽  
Tolulope Oke ◽  
Sarah Witherspoon
Keyword(s):  
Hochschild Cohomology ◽  
Tensor Products

Hochschild cohomology of tensor products of topological algebras

2010 ◽  
Vol 53 (2) ◽  
pp. 447-470
Author(s):  
Zinaida A. Lykova
Keyword(s):  
Hochschild Cohomology ◽  
Tensor Products ◽  
Cyclic Cohomology ◽  
Fréchet Spaces ◽  
Cohomology Groups ◽  
Topological Algebras ◽  
Kunneth Formula

AbstractWe describe explicitly the continuous Hochschild and cyclic cohomology groups of certain tensor products of $\widehat{\otimes}$-algebras which are Fréchet spaces or nuclear DF-spaces. To this end we establish the existence of topological isomorphisms in the Künneth formula for the cohomology of complete nuclear DF-complexes and in the Künneth formula for continuous Hochschild cohomology of nuclear $\widehat{\otimes}$-algebras which are Fréchet spaces or DF-spaces for which all boundary maps of the standard homology complexes have closed ranges.

scholarly journals Homotopy liftings and Hochschild cohomology of some twisted tensor products

2021 ◽  
pp. 2250238
Author(s):  
Pablo S. Ocal ◽  
Tolulope Oke ◽  
Sarah Witherspoon
Keyword(s):  
Tensor Product ◽  
Hochschild Cohomology ◽  
Tensor Products ◽  
Gerstenhaber Algebra ◽  
Graded Tensor Product

The Hochschild cohomology of a tensor product of algebras is isomorphic to a graded tensor product of Hochschild cohomology algebras, as a Gerstenhaber algebra. A similar result holds when the tensor product is twisted by a bicharacter. We present new proofs of these isomorphisms, using Volkov’s homotopy liftings that were introduced for handling Gerstenhaber brackets expressed on arbitrary bimodule resolutions. Our results illustrate the utility of homotopy liftings for theoretical purposes.

scholarly journals Tropical ideals do not realise all Bergman fans

2021 ◽  
Vol 8 (3) ◽  
Author(s):  
Jan Draisma ◽  
Felipe Rincón
Keyword(s):  
Tropical Geometry ◽  
Tensor Products ◽  
Tropical Variety ◽  
Polyhedral Complex ◽  
Direct Sum ◽  
Weight One ◽  
Polyhedral Complexes

AbstractEvery tropical ideal in the sense of Maclagan–Rincón has an associated tropical variety, a finite polyhedral complex equipped with positive integral weights on its maximal cells. This leads to the realisability question, ubiquitous in tropical geometry, of which weighted polyhedral complexes arise in this manner. Using work of Las Vergnas on the non-existence of tensor products of matroids, we prove that there is no tropical ideal whose variety is the Bergman fan of the direct sum of the Vámos matroid and the uniform matroid of rank two on three elements and in which all maximal cones have weight one.

scholarly journals The dual of the space of bounded operators on a Banach space

2021 ◽  
Vol 8 (1) ◽  
pp. 48-59
Author(s):  
Fernanda Botelho ◽  
Richard J. Fleming
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Banach Spaces ◽  
Dual Space ◽  
Tensor Products ◽  
Bounded Operators ◽  
Projective Tensor Product ◽  
Projective Tensor

Abstract Given Banach spaces X and Y, we ask about the dual space of the 𝒧(X, Y). This paper surveys results on tensor products of Banach spaces with the main objective of describing the dual of spaces of bounded operators. In several cases and under a variety of assumptions on X and Y, the answer can best be given as the projective tensor product of X ** and Y *.

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