Finitistic Dimensions of Monomial Algebras
نویسنده
چکیده
Theorem. (Auslander-Buchsbaum-Serre, 1956; see [2] and [24].) Let V be an affine algebraic variety over an algebraically closed field with coordinate ring R. Then the global dimension of R is finite if and only if V is smooth. If this is the case, then gl dimR = dimV . (That the global dimension of R is bounded above by n means that n-fold iteration of the process of taking syzygies of R-modules always leads to a projective module.)
منابع مشابه
A Quillen Model Structure Approach to the Finitistic Dimension Conjectures
We explore the interlacing between model category structures attained to classes of modules of finite X -dimension, for certain classes of modules X . As an application we give a model structure approach to the Finitistic Dimension Conjectures and present a new conceptual framework in which these conjectures can be studied. Let Λ be a finite dimensional algebra over a field k (or more generally...
متن کاملRecollements of derived categories III: finitistic dimensions
In this paper, we study homological dimensions of algebras linked by recollements of derived module categories, and establish a series of new upper bounds and relationships among their finitistic or global dimensions. This is closely related to a longstanding conjecture, the finitistic dimension conjecture, in representation theory and homological algebra. Further, we apply our results to a ser...
متن کاملMonomial Irreducible sln-Modules
In this article, we introduce monomial irreducible representations of the special linear Lie algebra $sln$. We will show that this kind of representations have bases for which the action of the Chevalley generators of the Lie algebra on the basis elements can be given by a simple formula.
متن کاملAn Upper Bound for the Finitistic Dimension of an Ei Category Algebra
EI categories can be thought of as amalgams of finite posets and finite groups and therefore the associated algebras are built up from incidence algebras and group algebras of finite groups. For this particular class of algebras we construct an upper bound for the finitistic dimension.
متن کاملHochschild Homology and Split Pairs
We study the Hochschild homology of algebras related via split pairs, and apply this to fibre products, trivial extensions, monomial algebras, graded-commutative algebras and quantum complete intersections. In particular, we compute lower bounds for the dimensions of both the Hochschild homology and cohomology groups of quantum complete intersections.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2007