ﻻ يوجد ملخص باللغة العربية
The set of associative and commutative hypercomplex numbers, called the perfect hypercomplex algebra (PHA) is investigated. Necessary and sufficient conditions for an algebra to be a PHA via semi-tensor product(STP) of matrices are reviewed. The zero set is defined for non-invertible hypercomplex numbers in a given PHA, and a characteristic function is proposed for calculating zero set. Then PHA of different dimensions are considered. First, $2$-dimensional PHAs are considered as examples to calculate their zero sets etc. Second, all the $3$-dimensional PHAs are obtained and the corresponding zero sets are investigated. Third, $4$-dimensional or even higher dimensional PHAs are also considered. Finally, matrices over pre-assigned PHA, called perfect hypercomplex matrices (PHMs) are considered. Their properties are also investigated.
This paper studies commuting matrices in max algebra and nonnegative linear algebra. Our starting point is the existence of a common eigenvector, which directly leads to max analogues of some classical results for complex matrices. We also investigat
Let $mathfrak{sp}_{2n}(mathbb {K})$ be the symplectic Lie algebra over an algebraically closed field of characteristic zero. We prove that for any nonzero nilpotent element $X in mathfrak{sp}_{2n}(mathbb {K})$ there exists a nilpotent element $Y in m
We identify the dimension of the centralizer of the symmetric group $mathfrak{S}_d$ in the partition algebra $mathcal{A}_d(delta)$ and in the Brauer algebra $mathcal{B}_d(delta)$ with the number of multidigraphs with $d$ arrows and the number of disj
2-local derivation is a generalized derivation for a Lie algebra, which plays an important role to the study of local properties of the structure of the Lie algebra. In this paper, we prove that every 2-local derivation on the conformal Galilei algebra is a derivation.
Evolution algebras are non-associative algebras that describe non-Mendelian hereditary processes and have connections with many other areas. In this paper we obtain necessary and sufficient conditions for a given algebra $A$ to be an evolution algebr