The main result of this paper is a generalization the theorem Chevalley-Shephard-Todd to rings invariants pseudoreflection groups over Dedekind domains. In special case principal ideal domain in which group order invertible it proved that ring isomorphic polynomial ring. An intermediate every finitely generated regular graded algebra tensor product blowup algebras.

We prove that every positive trace on a countably generated ∗-algebra can be approximated by positive traces on algebras of generic matrices. This implies that every countably generated tracial ∗-algebra can be embedded into a metric ultraproduct of generic matrix algebras. As a particular consequence, every finite von Neumann algebra with separable pre-dual can be embedded into an ultraproduct...

Abstract. Quantum symmetric algebras (or noncommutative polynomial rings) arise in many places in mathematics. In this article we find the multiplicative structure of their Hochschild cohomology when the coefficients are in an arbitrary bimodule algebra. When this bimodule algebra is a finite group extension (under a diagonal action) of a quantum symmetric algebra, we give explicitly the graded...

Summary The article concerns about formalizing multivariable formal power series and polynomials [3] in one variable terms of “bag” (as described detail [9]), the same notion as multiset over a finite set, Mizar system [1], [2]. Polynomial rings ring series, both variable, have been formalized [6], [5] respectively, elements these are represented by infinite sequences scalars. On other hand, fo...

Roughly speaking, a separating algebra is a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this paper, we introduce a more geometric notion of separating algebra. This allows us to prove that when there is a polynomial separating algebra, the group is generated by reflections, and when there is a complete int...

For $X$ a smooth scheme acted on by linear algebraic group $G$ and $p$ prime, the equivariant Chow ring $CH^*_G(X)\otimes \mathbb{F}_p$ is an unstable algebra over Steenrod algebra. We compute Lannes's $T$-functor applied to \mathbb{F}_p$. As application, we localization of away from $n$-nilpotent modules algebra, affirming conjecture Totaro as special case. The case when point $n = 1$ generali...

was described in terms of the so-called Hall algebra U+X of the category of coherent sheaves on an elliptic curve X (defined over a finite field Fq). This Hall algebra turns out to be a two-parameter deformation of ΛΛ, the two deformation parameters being the Frobenius eigenvalues σ, σ̄ of the particular elliptic curve. In fact, the structure constants for U+X are Laurent polynomials in σ and σ̄,...

There are also four appendices. Let K be a field of characteristic 0, and let C be a commutative K-algebra. which makes C into a Lie algebra, and is a biderivation (i.e. a derivation in each argument). The pair C, {−, −} is called a Poisson algebra. Poisson brackets arise in several ways. Example 1.1. Classical Hamiltonian mechanics. Here K = R, X is an even dimensional differentiable manifold ...

By a generalized Tannaka-Krein reconstruction we associate to the admissible representions of the category O of a Kac-Moody algebra, and its category of admissible duals a monoid with a coordinate ring. The Kac-Moody group is the Zariski open dense unit group of this monoid. The restriction of the coordinate ring to the Kac-Moody group is the algebra of strongly regular functions introduced by ...

In our report on the first “Derived Category Methods in Commutative Algebra” workshop (2008) we wrote: “Derived category methods have proved to be very successful in ring theory, in particular in commutative algebra. Evidence is provided by [1, 8, 4, 5, 6, 7, 11, 12, 15, 16, 19, 20, 23, 24, 27], to list some work of considerable importance. Surprisingly, there is no accessible introduction or r...