arXiv subjects
Publications and source records attributed to Yuji Kobayashi.
We study general properties of multipliers and weak multipliers of algebras. We apply the results to determine the (weak) multipliers of associative algebras and zeropotent algebras of dimension 3 over an algebraically closed field.
For a nonsingular matrix $A$, we propose the form $Tr(^t\!A A^{-1})$, the trace of the product of its transpose and inverse, as a new invariant under congruence of nonsingular matrices.
We provide a complete classification of three-dimensional associative algebras over the real and complex number fields based on a complete elementary proof. We list up all the multiplication tables of the algebras up to isomorphism. We compare our results with those given by mathematicians in the 19th century.
We further develop the reduced action formalism of the SU(2)-Higgs model originally given by Aoyama et.al.. Our new ansatz for the sphaleron solution makes it possible to apply this formalism to all range of the Higgs self coupling constant. Based on the formalism, we construct a bounce solution oscillating around the sphaleron.