On the Homological Dimension of Algebras of Differential Operators
Titel:
On the Homological Dimension of Algebras of Differential Operators
Auteur:
Chase, Stephen U.
Verschenen in:
Communications in algebra
Paginering:
Jaargang 1 (1974) nr. 5 pagina's 351-363
Jaar:
1974
Inhoud:
Let A be a commutative algebra over a field k, and VA be the k-subalgebra of Endk(A) generated by EndA(A) = A and all k-derivations of A. A study of the homological properties of VA was initiated by Hochschild, Kostant, and Rosenberg in [5], and continued by Rinehart [8], [9], Roos [11], Bjork [1], Rinehart and Rosenberg [10], and others. It was proved in [5] that, if k is perfect and A is a regular affine algebra of dimension r, then the global dimension of VA is between r and 2r. Moreover, if k has positive characteristic, then gl.dim VA = 2r [8]. By a recent celebrated theorem of Roos [11], gl.dim VA = r if k has characteristic zero and A = k[x1, …, xr]; in this case VA is the so-called “Weyl algebra on 2r variables”.
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