scholarly journals Isomorphisms of tensor algebras arising from weighted partial systems

2018 ◽  
Vol 370 (5) ◽  
pp. 3507-3549 ◽  
Author(s):  
Adam Dor-On
Keyword(s):  
Tensor Algebras ◽  
Partial Systems

scholarly journals GRADED TWISTED CALABI–YAU ALGEBRAS ARE GENERALIZED ARTIN–SCHELTER REGULAR

2021 ◽  
pp. 1-54
Author(s):  
MANUEL L. REYES ◽  
DANIEL ROGALSKI
Keyword(s):  
Regularity Property ◽  
Graded Algebra ◽  
General Study ◽  
Locally Finite ◽  
Tensor Algebras ◽  
Finite Dimensional ◽  
Dimension 2 ◽  
Separable Algebras ◽  
Gk Dimension

Abstract This is a general study of twisted Calabi–Yau algebras that are $\mathbb {N}$ -graded and locally finite-dimensional, with the following major results. We prove that a locally finite graded algebra is twisted Calabi–Yau if and only if it is separable modulo its graded radical and satisfies one of several suitable generalizations of the Artin–Schelter regularity property, adapted from the work of Martinez-Villa as well as Minamoto and Mori. We characterize twisted Calabi–Yau algebras of dimension 0 as separable k-algebras, and we similarly characterize graded twisted Calabi–Yau algebras of dimension 1 as tensor algebras of certain invertible bimodules over separable algebras. Finally, we prove that a graded twisted Calabi–Yau algebra of dimension 2 is noetherian if and only if it has finite GK dimension.

Piecewise Hereditary Triangular Matrix Algebras

2021 ◽  
Vol 28 (01) ◽  
pp. 143-154
Author(s):  
Yiyu Li ◽  
Ming Lu
Keyword(s):  
Positive Integer ◽  
Triangular Matrix ◽  
Derived Categories ◽  
Matrix Algebras ◽  
Tensor Algebras ◽  
Finite Dimensional ◽  
Abelian Categories ◽  
Upper Triangular Matrix ◽  
Orbit Categories ◽  
Finite Dimensional Algebras

For any positive integer [Formula: see text], we clearly describe all finite-dimensional algebras [Formula: see text] such that the upper triangular matrix algebras [Formula: see text] are piecewise hereditary. Consequently, we describe all finite-dimensional algebras [Formula: see text] such that their derived categories of [Formula: see text]-complexes are triangulated equivalent to derived categories of hereditary abelian categories, and we describe the tensor algebras [Formula: see text] for which their singularity categories are triangulated orbit categories of the derived categories of hereditary abelian categories.

Tensor algebras

2013 ◽  
pp. 57-91
Author(s):  
Jan Derezinski ◽  
Christian Gerard
Keyword(s):  
Tensor Algebras

scholarly journals The hyperrigidity of tensor algebras of C⁎-correspondences

2020 ◽  
Vol 483 (1) ◽  
pp. 123611 ◽  
Author(s):  
Elias G. Katsoulis ◽  
Christopher Ramsey
Keyword(s):  
Tensor Algebras

scholarly journals Amenability and weak amenability of tensor algebras and algebras of nuclear operators

1991 ◽  
Vol 51 (3) ◽  
pp. 483-488 ◽  
Author(s):  
Niels Grønbaek
Keyword(s):  
Tensor Algebra ◽  
Tensor Algebras ◽  
Canonical Map ◽  
Weak Amenability ◽  
Nuclear Operators ◽  
Finite Dimensional

AbstractLet E and F constitute a Banach pairing. We prove that the algebra of F-nuclear operators on E, Nf (E), is amenable if and only if E is finite dimensional and is weakly amenable if and only if dim KF ≦ 1, and the trace on E⊗F is injective on KF. Here KF is the kernel of the canonical map E⊗^F →NF(E). On the route we find the corresponding statements for the associated tensor algebra, E⊗^F.

Sign in / Sign up

Export Citation Format

Share Document