In this article, topologies on metagroups and quasigroups are studied. Topologies smashed twisted wreath products of scrutinized, which making them topological metagroups. For purpose, transversal sets As a tool for this, semi-direct also investigated. They have specific features in comparison with groups because the nonassociativity, general, A related structure is Particularly, their compact ...

In this paper we will consider noncommutativity that arises from bosonic T-dualization of type II superstring in presence Ramond-Ramond (RR) field, which linearly depends on the coordinates x ? $x^\mu$ . The derivative RR field C ? ? $C^{\alpha \beta }_\mu$ is infinitesimal. We employ generalized Buscher procedure can be applied to cases have coordinate dependent background fields. Bosonic part...

this paper extends the scope of algebraic computation based on a non standard × to the more basic case of a non standard +, where standard means associative and commutative. two physically meaningful examples of a non standard + are provided by the observation of motion in special relativity, from either outside (3d) or inside (2d or more), we revisit the “gyro”-theory of ungar to present the m...

This is ongoing work on hypercomputation [4]. We revisit the works of Dickson [5] and Mahler [9] on integral octonions. Nonassociativity (in the form of alternativity) leads to the unexpected consequence that the theorem of (at most) 4 squares (Bachet – Lagrange) becomes a theorem of (exactly) 1, 2 or 4 identical squares for a subset of N∗. These numbers measure the norm of the vectors in the D...

We give some examples of nonassociative algebras which occur in VOA theory and finite group theory. A good theory of these algebras could be useful.