Daniel R. Farkas

Synergy in the theories of Gröbner bases and path algebras

A general theory for Grobner basis in path algebras is introduced which extends the known theory for commutative polynomial rings and free associative algebras

K0 and noetherian group rings

Abstract The authors use K -theoretic methods to prove that if F is a field of char 0 and G is a torsion free polycyclic-by-finite-group then F [ G ] is a domain.

Ring theory from symplectic geometry

Abstract Basic results for an algebraic treatment of commutative and noncommutative Poisson algebras are described. Symplectic algebras are examined from a ring-theoretic point of view.

Algebras which are nearly finite dimensional and their identities

Suppose that all the nonzero one-sided or two-sided ideals of an algebra have finite codimension. To what extent must the algebra be p.i. or primitive?

Poisson polynomial identities II

Abstract. We study Poisson polynomial identities for the symmetric Poisson algebra of a Lie algebra and for the graded Poisson algebra associated to a ring of differential operators. Connections are made among degrees of identities, coadjoint orbits and Krull dimension.

The Anick resolution

Abstract The Anick resolution for associative algebras is given an explicit, combinatorial description.

Diagonalizable derivations of finite-dimensional algebras I

Diagonalizable derivations of a finite-dimensional algebra usually span an ideal in the Lie algebra of all derivations. This ideal is studied for underlying graded, monomial, and path algebras.

A Ring-Theorist's Description of Fedosov Quantization

We present a formal, algebraic treatment of Fedosovs argument that the coordinate algebra of a symplectic manifold has a deformation quantization. His remarkable formulas are established in the context of affine symplectic algebras.

Modules for poisson algebras

Notions of Poisson module axe discussed with the goal of characterizing those noetherian Poisson algebras all of whose finitely generated Poisson modules are projective. 1991 MSC: 16R, 16W, 17B60.

Finite Group Actions on Poisson Algebras

Let Andenote the Weyl algebra of all differential operators on the polynomial algebra C[X1,… Xn].It is well known that if G is a finite group of algebra automorphisms of An, then An is a simple algebra. (See [12] pp. 20–23 for an algebraic proof or [15] Lemma 1.2 for an analytic approach.) It is natural to expect that the analogous result holds for the associated graded object. To be precise, if Anis filtered by total degree, then the associated graded algebra is the larger polynomial ring R = C[X1, …Xn,Y1,… Yn]with the Poisson bracket which describes a standard symplectic affine space. To be explicit R is also a Lie algebra subject to