Related papers: Higher-Dimensional Loop Algebras, Non-Abelian Exte…
We introduce \textit{Niebrzydowski algebras}, algebraic structures with a ternary operation and a partially defined multiplication, with axioms motivated by the Reidemeister moves for $Y$-oriented trivalent spatial graphs and…
We present a unified and completely general formulation of extended geometry, characterised by a Kac-Moody algebra and a highest weight coordinate module. Generalised diffeomorphisms are constructed, as well as solutions to the section…
The theory of operads (May, cyclic, modular, PROPs, etc) is extended to include higher dimensional phenomena, i.e. operations between operations, mimicking the algebraic structure on varieties of arbitrary dimensions, having marked…
Using 3-algebras we obtain a nonabelian system of equations that furnish a representation of the (2,0)-supersymmetric tensor multiplet. The on-shell conditions are quite restrictive so that the system can be reduced to five-dimensional…
We prove some conditions for the existence of higher dimensional algebraic fibering of group extensions. This leads to various corollaries on incoherence of groups and some geometric examples of algebraic fibers of type $F_n$ but not…
We consider a generalisation of vector fields on a vector space, where the vector space is generalised to a highest-weight module over a Kac-Moody algebra. The generalised vector field is an element in a non-associative superalgebra defined…
In this paper we generalize some of these results for loop algebras and groups as well as for the Virasoro algebra to the two-dimensional case. We define and study a class of infinite dimensional complex Lie groups which are central…
We introduce the umbral calculus formalism for hypercomplex variables starting from the fact that the algebra of multivariate polynomials $\BR[\underline{x}]$ shall be described in terms of the generators of the Weyl-Heisenberg algebra. The…
We present an action for a six-dimensional superconformal field theory containing a non-abelian tensor multiplet. All of the ingredients of this action have been available in the literature. We bring these pieces together by choosing the…
We briefly review the essential points of our recent work in non-Abelian T-duality. In particular, we show how non-abelian T-duals can effectively describe infinitely high spin sectors of a parent theory and how to implement the…
Nonlinear equations of $p$-branes in $D=(2p+1)$-dimensional Minkowski space are discussed. Presented are new exact solutions for a set of spinning $p$-branes with $p=2,3,...,(D-1)/2$ and the Abelian symmetries $U(1)\times U(1)\times...…
The division algebras R, C, H, O are used to construct and analyze the N=1,2,4,8 supersymmetric extensions of the KdV hamiltonian equation. In particular a global N=8 super-KdV system is introduced and shown to admit a Poisson bracket…
An action for a prospect of a $p$-adic open superstring on a target Minkowski space is proposed. The action is constructed for `worldsheet' fields taking values in the $p$-adic field $\mathbb{Q}_p$, but it is assumed to be obtained from a…
While string or Yang-Mills theories are based on Lie algebra or two-algebra structure, recent studies indicate that M-theory may require a one higher, three-algebra structure. Here we construct a covariant action for a supermembrane in…
We consider the extended superconformal algebras of the Knizhnik-Bershadsky type with $W$-algebra like composite operators occurring in the commutation relations, but with generators of conformal dimension 1,$\frac{3}{2}$ and 2, only. These…
We construct finite-dimensional Hopf algebras whose coradical is the group algebra of a central extension of an abelian group. They fall into families associated to a semisimple Lie algebra together with a Dynkin diagram automorphism. We…
There is a long-standing problem of algebra to extend the symmetric monoidal structure of abelian groups, given by the tensor product, to a non abelian setting. In this paper we show that such an extension is possible. Morover our non…
The standard notion of the non-Abelian duality in string theory is generalized to the class of $\si$-models admitting `non-commutative conserved charges'. Such $\si$-models can be associated with every Lie bialgebra $(\cg ,\cgt)$ and they…
We consider the recursion operators with nonlocal terms of special form for evolution systems in (1+1) dimensions, and extend them to well-defined operators on the space of nonlocal symmetries associated with the so-called universal Abelian…
We develop a theory of `non-abelian higher special elements' in the non-commutative exterior powers of the Galois cohomology of $p$-adic representations. We explore their relation to the theory of organising matrices and thus to the Galois…