Zobrazeno 1 - 10
of 194
pro vyhledávání: '"17D05"'
Autor:
Feldvoss, Jörg, Wagemann, Friedrich
In this paper we define three different notions of tensor products for Leibniz bimodules. The ``natural" tensor product of Leibniz bimodules is not always a Leibniz bimodule. In order to fix this, we introduce the notion of a weak Leibniz bimodule an
Externí odkaz:
http://arxiv.org/abs/2411.01044
Autor:
Ghiloni, Riccardo, Stoppato, Caterina
This work proposes a unified theory of regularity in one hypercomplex variable: the theory of $T$-regular functions. In the special case of quaternion-valued functions of one quaternionic variable, this unified theory comprises Fueter-regular functio
Externí odkaz:
http://arxiv.org/abs/2408.01523
Autor:
Panasenko, A. S.
All Rota-Baxter operators of weight zero on split octonion algebra over a~field of characteristic not 2 are classified up to conjugation by automorphisms and antiautomorphisms. Thus, the classification of Rota-Baxter operators on composition algebras
Externí odkaz:
http://arxiv.org/abs/2406.16312
Autor:
Aryapoor, Masood, Bäck, Per
Publikováno v:
J. Algebra 662 (2025), pp. 482-501
We introduce and study flipped non-associative polynomial rings. In particular, we show that all Cayley-Dickson algebras naturally appear as quotients of a certain type of such rings; this extends the classical construction of the complex numbers (an
Externí odkaz:
http://arxiv.org/abs/2403.03763
Autor:
Guterman, Alexander, Zhilina, Svetlana
We introduce the classes of descendingly flexible and descendingly alternative algebras over an arbitrary field $\mathbb{F}$. We suggest a new method based on the sequence of differences between the dimensions of the linear spans of words, which allo
Externí odkaz:
http://arxiv.org/abs/2312.03170
Roots and right factors of polynomials and left eigenvalues of matrices over Cayley-Dickson algebras
Autor:
Chapman, Adam, Vishkautsan, Solomon
Publikováno v:
Communications in Mathematics, Volume 33 (2025), Issue 3 (Special issue: European Non-Associative Algebra Seminar) (February 27, 2024) cm:12613
Over a composition algebra $A$, a polynomial $f(x) \in A[x]$ has a root $\alpha$ if and only $f(x)=g(x)\cdot (x-\alpha)$ for some $g(x) \in A[x]$. We examine whether this is true for general Cayley-Dickson algebras. The conclusion is that it is when
Externí odkaz:
http://arxiv.org/abs/2311.16704
Autor:
Pchelintsev, S. V., Shestakov, I. P.
It is proved that for any natural number $n$ the subalgebra of a free finitely generated alternative algebra generated by all the words on generators whose length is a multiple of $n$ (the Veronese $n$-subalgebra), is finitely generated.
Externí odkaz:
http://arxiv.org/abs/2311.14441
In this paper we discuss some basic properties of octonionic Bergman and Hardy spaces. In the first part we review some fundamental concepts of the general theory of octonionic Hardy and Bergman spaces together with related reproducing kernel functio
Externí odkaz:
http://arxiv.org/abs/2311.07691
The associative Cayley-Dickson algebras over the field of real numbers are also Clifford algebras. The alternative but nonassociative real Cayley-Dickson algebras, notably the octonions and split octonions, share with Clifford algebras an involutary
Externí odkaz:
http://arxiv.org/abs/2310.09972
Autor:
Hildebrandsson, Victor
Octonion algebras are certain algebras with a multiplicative quadratic form. In their 2019 article, Alsaody and Gille show that, for octonion algebras over unital commutative rings, there is an equivalence between isotopes and isometric quadratic for
Externí odkaz:
http://arxiv.org/abs/2309.01776