9 papers
On the relation of the monomial group with other algebraic structures
Igor Bayak
It is shown in what way monomial group connects Abelian group Z^{n} and total linear group GL(n). It is shown that any subgroup of Abelian group Z^{n} induces subgroup of monomial…
On the geometry of plasma reactor
I. V. Bayak
It is presented the concept of controled nuclear synthesis in top of cone formed by rotational dynamic flow of low-temperature plasma.
On the interior structure of exterior algebra
I. V. Bayak
It is constructed the functor from category of product linear space to category of skew-symmetric tensor space. It is defined and described the bound bundle as analog of a symplex…
On some mathematical construction of many-dimensional cosmos
I. V. Bayak
It is shown that classical Clifford algebras are group algebras of cyclic subgroups of arrowy rermutations. It is established that Euclidean 3-space, Pauli and Dirac algebras and g…
On the rigid algebraic structure of Euclidean spaces
I. V. Bayak
It is shown that the groups of automorphisms of Euclidean spaces are isomorphic to the groups of topologic automorphisms of respectively factored arithmetic spaces. In particular,…
On the generation of linear groups by combinatoric groups
I. V. Bayak
It is described the group of arrowy permutations (that is extension of symmetric group) and the consequent process of generation of GL(n) and some its subgroups by this combinatori…