A commutative local Cohen-Macaulay ring R of finite Cohen-Macaulay type is known to be an isolated singularity; that is, Spec(R) \ {m} is smooth. This paper proves a non-commutative analogue. Namely, if A is a (non-commutative) graded Artin-Schelter Cohen-Macaulay algebra which is FBN and has finite Cohen-Macaulay type, then the non-commutative projective scheme determined by A is smooth.

The maximal dimension of a commutative subalgebra of the Grassmann algebra is determined. It is shown that for any commutative subalgebra there exists an equidimensional commutative subalgebra spanned by monomials. It follows that the maximal dimension of a commutative subalgebra can be expressed in terms of the maximal size of an intersecting system of subsets of odd size in a finite set. 2010...

Let G be a connected reductive group acting on a finite dimensional vector space V . Assume that V is equipped with a G-invariant symplectic form. Then the ring O(V ) of polynomial functions becomes a Poisson algebra. The ring O(V ) of invariants is a sub-Poisson algebra. We call V multiplicity free if O(V ) is Poisson commutative, i.e., if {f, g} = 0 for all invariants f and g. Alternatively, ...

Following ideas of Pirashvili, we define higher order Hochschild cohomology over spheres S defined for any commutative algebra A and module M . When M = A, we prove that this cohomology is equipped with graded commutative algebra and degree d Lie algebra structures as well as with Adams operations. All operations are compatible in a suitable sense. These structures are related to Brane topology...

A result of Artin, Small, and Zhang is used to show that a noetherian algebra over a commutative, noetherian Jacobson ring will be Jacobson if the algebra possesses a locally finite, noetherian associated graded ring. This result is extended to show that if an algebra over a commutative noetherian ring has a locally finite, noetherian associated graded ring, then the intersection of the powers ...

In this thesis, I present an associative diagram algebra that is a faithful representation of a particular Temperley–Lieb algebra of type affine C, which has a basis indexed by the fully commutative elements of the Coxeter group of the same type. The Coxeter group of type affine C contains an infinite number of fully commutative elements, and so the corresponding Temperley–Lieb algebra is of in...

The standard reduced bar complex B(A) of a differential graded algebra A inherits a natural commutative algebra structure if A is a commutative algebra. We address an extension of this construction in the context of E-infinity algebras. We prove that the bar complex of any E-infinity algebra can be equipped with the structure of an E-infinity algebra so that the bar construction defines a funct...