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Inertial law of quadratic forms on modules over plural algebra

Marek Jukl — 1995

Mathematica Bohemica

Quadratic forms on a free finite-dimensional module are investigated. It is shown that the inertial law can be suitably generalized provided the vector space is replaced by a free finite-dimensional module over a certain linear algebra over ( real plural algebra) introduced in [1].

Geometry of Cyclic and Anticylic Algebras

Igor M. BurlakovMarek Jukl — 2016

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The article deals with spaces the geometry of which is defined by cyclic and anticyclic algebras. Arbitrary multiplicative function is taken as a fundamental form. Motions are given as linear transformation preserving given multiplicative function.

Hypercomplex Algebras and Geometry of Spaces with Fundamental Formof an Arbitrary Order

Mikhail P. BurlakovIgor M. BurlakovMarek Jukl — 2016

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The article is devoted to a generalization of Clifford and Grassmann algebras for the case of vector spaces over the field of complex numbers. The geometric interpretation of such generalizations are presented. Multieuclidean geometry is considered as well as the importance of it in physics.

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