Related papers: Mui invariants and Milnor operations

Hilbert(ian) A-modules over finite von Neumann algebras A with a faithful normal trace state (from global analysis) and Hilbert W*-modules over A (from operator algebra theory) are compared, and a categorical equivalence is established. The…

We determine the abelian invariants of the maximal tori in the finite spin groups of type $D_l$

We extend the notion of the $J$-invariant to arbitrary semisimple linear algebraic groups and provide complete decompositions for the normed Chow motives of all generically quasi-split twisted flag varieties. Besides, we establish some…

Trigonometric invariants are defined for each Weyl group orbit on the root lattice. They are real and periodic on the coroot lattice. Their polynomial algebra is spanned by a basis which is calculated by means of an algorithm. The…

We prove finite generation of the algebras of invariants for a class of linear actions of suitable non-reductive groups on projective and affine varieties, and give a geometric construction for their GIT quotients.

It is proved that for any finite dimensional representation of a prime order group over the field of rational numbers, polynomial invariants of degree at most $3$ separate the orbits. A result providing an upper degree bound for separating…

In this paper we introduce the systematic study of invariant functions and equivariant mappings defined on Minkowski space under the action of the Lorentz group. We adapt some known results from the orthogonal group acting on the Euclidean…

We give criteria for real, complex and quaternionic representations to define s-representations, focusing on exceptional Lie algebras defined by spin representations. As applications, we obtain the classification of complex representations…

In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact algebras sp(n,R), in detail for n=6. Our choice of these algebras is motivated by the fact that…

We classify actions of generalized Taft algebras on preprojective algebras of extended Dynkin quivers of type $A$. This may be viewed as an extension of the problem of classifying actions on the polynomial ring in two variables. In cases…

Invariants allow to classify images up to the action of a group of transformations. In this paper we introduce notions of the algebras of simultaneous polynomial and rational 2D moment invariants and prove that they are isomorphic to the…

Let $E$ be a elementary abelian $p$-group of order $q=p^n$. Let $W$ be a faithful indecomposable representation of $E$ with dimension 2 over a field $k$ of characteristic $p$, and let $V= S^m(W)$ with $m<q$. We prove that the rings of…

Polynomial invariants of a group action often appear only in high degree, and in many representations the invariant ring imposes severe degree constraints before any nontrivial invariants can occur. In contrast, the larger class of unitary…

We classify quantum analogues of actions of finite subgroups G of SL_2(k) on commutative polynomial rings k[u,v]. More precisely, we produce a classification of pairs (H,R), where H is a finite dimensional Hopf algebra that acts inner…

We characterize, in an algebraic and in a diagrammatic way, Milnor string link invariants indexed by sequences where any index appears at most $k$ times, for any fixed $k\ge 1$. The algebraic characterization is given in terms of an…

Dunkl operators for complex reflection groups are defined in this paper. These commuting operators give rise to a parametrized family of deformations of the polynomial De Rham complex. This leads to the study of the polynomial ring as a…

We compute some numerical invariants of local cohomology of the ring of invariants by a finite group, mainly in the modular case. Also, we present some applications. In particular, we study Cohen-Macaulay property of modular invariants from…

We revisit the linearization theorems for proper Lie groupoids around general orbits (statements and proofs). In the the fixed point case (known as Zung's theorem) we give a shorter and more geometric proof, based on a Moser deformation…

Using the language of operated algebras, we construct and investigate a class of operator rings and enriched modules induced by a derivation or Rota-Baxter operator. In applying the general framework to univariate polynomials, one is led to…

In this paper we develop a theory of class invariants associated to $p$-adic representations of absolute Galois groups of number fields. Our main tool for doing this involves a new way of describing certain Selmer groups attached to…