Related papers: Combinatorial invariants of algebraic Hamiltonian …

Based on a fact that complex Clifford algebras of even dimension are isomorphic to the matrix ones, we consider bundles in Clifford algebras whose structure group is a general linear group acting on a Clifford algebra by left…

We demonstrate that from the first order formulation of the Einstein-Cartan action it is possible to derive the basic differential identity that leads to translational invariance of the action in the tangent space. The transformations of…

A global action is the algebraic analogue of a topological manifold. This construction was introduced in first place by A. Bak as a combinatorial approach to K-Theory and the concept was later generalized by Bak, Brown, Minian and Porter to…

In a natural way, the local diffeomorphisms of a manifold onto itself act on the reference frame bundles of any order and on the bundles associated with them. Due to the transitivity, the invariants by diffeomorphisms of an associated…

We consider abelian gauge theories on a lattice and develop properties of an axial gauge that is covariant under lattice symmetries. Particular attention is paid to a version that behaves nicely under block averaging renormalization group…

We introduce equivariant Burnside groups, new invariants in equivariant birational geometry, generalizing birational symbols groups for actions of finite abelian groups, due to Kontsevich, Pestun, and the second author, and study their…

In this manuscript, we define the notion of linearly reductive groups over commutative unital rings and study the Cohen-Macaulay property of the ring of invariants under rational actions of a linearly reductive group. Moreover, we study the…

Here we shall consider the topology and dynamics associated to a wide class of matchbox manifolds, including a large selection of tiling spaces and all minimal matchbox manifolds of dimension one. For such spaces we introduce topological…

Given a group action, known by its infinitesimal generators, we exhibit a complete set of syzygies on a generating set of differential invariants. For that we elaborate on the reinterpretation of Cartan's moving frame by Fels and Olver…

We study the symmetry group of the geodesic equations of the spatial solutions of the space-time generated by a noninertial rotating system of reference. It is a seven dimensional Lie group, which is neither solvable nor nilpotent. The…

The smooth action of a compact Lie group on a compact manifold can be resolved to an iterated space, as made explicit by Pierre Albin and the second author. On the resolution the lifted action has fixed isotropy type, in an iterated sense,…

We study Hamiltonian field theories on the multisymplectic bundle of a principal G-bundle with Hamiltonian densities invariant under a subgroup $H\subset G$. Using the covariant bracket formulation, we reduce the polysymplectic space and…

The deep interconnection between linear algebra and graph theory allows one to interpret classical matrix invariants through combinatorial structures. To each square matrix A over a commutative ring K, one can associate a weighted directed…

We investigate involutive, non-combinatorial solutions of the braid equation viewed as special deformations of the permutation map. By employing these solutions, we identify the associated quantum algebra, which we introduce as the…

We investigate G-invariant symplectic structures on the cotangent bundle T*P of a principal G-bundle P(M,G) which are canonically related to automorphisms of the tangent bundle TP covering the identity map of P and commuting with the action…

A theorem of Gerald Schwarz [24, Thm. 1] says that for a linear action of a compact Lie group $G$ on a finite dimensional real vector space $V$ any smooth $G$-invariant function on $V$ can be written as a composite with the Hilbert map. We…

We present two hypermatrix formulations of the Cayley Hamilton theorem. One of the proposed formulation naturally extends to hypermatrices the combinatorial interpretations of the classical Cayley Hamilton theorem. We conclude by discussing…

We study properties of irreducible and completely reducible representations of finitely generated groups Gamma into reductive algebraic groups G in in the context of the geometric invariant theory of the G-action on Hom(Gamma,G) by…

Let $Y$ be an irreducible non-singular affine $G$-variety with a $2$-large action. We show that the Hamiltonian reduction $T^*Y/\!\!/\!\!/G$ is a symplectic variety with terminal singularities, isomorphic to the affine closure of…

Let $M$ be complex projective manifold and $A$ a positive line bundle on it. Assume that a compact and connected Lie group $G$ acts on $M$ in a Hamiltonian and holomorphic manner and that this action linearizes to $A$. Then, there is an…