For a space X, we define Frobenius and Verschiebung operations on the nil-terms NAfd ± (X) in the algebraic K-theory of spaces, in three different ways. Two applications are included. Firstly, we obtain that the homotopy groups of NAfd ± (X) are either trivial or not finitely generated as abelian groups. Secondly, the Verschiebung defines a Z[N×]-module structure on the homotopy groups of NAfd ...

To any Frobenius superalgebra $A$ we associate towers of nilCoxeter algebras and nilHecke algebras. These act naturally, via divided difference operators, on polynomial When is the ground ring, our recover classical two-dimensional Clifford algebra, they are Morita equivalent to odd

We prove a non conventional pointwise convergence theorem for a nilsystem, and give an explicit formula for the limit.

M. NILS PETERSON,∗ MARKUS J. PETERSON,† AND TARLA RAI PETERSON‡ ∗Center for Systems Integration and Sustainability, Michigan State University, 13 Natural Resources Building, East Lansing, MI 48824-1222, U.S.A., email [email protected] †Department of Wildlife and Fisheries Sciences, Texas A&M University, College Station, TX 77843-2258, U.S.A. ‡Department of Communication, Program in Peace & Confl...

Every commutative nil-semigroup of index 2 can be imbedded into such a semigroup without irreducible elements.

In this paper, we study biharmonic maps into Sol and Nil spaces, two model spaces of Thurston's 3-dimensional geometries. We characterize non-geodesic biharmonic curves in Sol space and prove that there exists no non-geodesic biharmonic helix in Sol space. We also show that a linear map from a Eu-clidean space into Sol or Nil space is biharmonic if and only if it is a harmonic map, and give a c...

A geometric transition is a continuous path of geometric structures that changes type, meaning that the model geometry, i.e. the homogeneous space on which the structures are modeled, abruptly changes. In order to rigorously study transitions, one must define a notion of geometric limit at the level of homogeneous spaces, describing the basic process by which one homogeneous geometry may transf...