Zobrazeno 1 - 10
of 119
pro vyhledávání: '"17A45"'
Autor:
Stroppel, Markus J.
We construct a model of the Hermitian unital of order 3 (obtained from the non-degenerate hermitian form in three variables over the field of order 9) inside the octonion algebra over the field of order 2. This construction is invariant under the aut
Externí odkaz:
http://arxiv.org/abs/2412.09081
Every non-solvable and non-semisimple quadratic Lie algebra can be obtained as a double extension of a solvable quadratic Lie algebra. Thanks to a partial classification of nilpotent Lie algebras and this result, we can design different techniques to
Externí odkaz:
http://arxiv.org/abs/2401.14348
The procedure of double extension of vector spaces endowed with non-degenerate bilinear forms allows us to introduce the class of generalized $\mbK$-oscillator algebras over any arbitrary field $\mbK$. Starting from basic structural properties of suc
Externí odkaz:
http://arxiv.org/abs/2401.03100
Autor:
Yahaghi, Bamdad R.
In this paper, we consider real and complex algebras as well as algebras over general fields. In Section 2, we revisit and prove several results on (quadratic) algebras over general fields. In Section 3, we show how to develop the spectral theory in
Externí odkaz:
http://arxiv.org/abs/2401.00985
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
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:
Hamza, Oussama
We introduce a criterion on the presentation of finitely presented pro-$p$ groups which allows us to compute their cohomology groups and infer quotients of mild groups of cohomological dimension strictly larger than two. We interpret these groups as
Externí odkaz:
http://arxiv.org/abs/2309.06396
Autor:
Chapman, Adam, Levin, Ilan
Publikováno v:
Communications in Mathematics, Volume 32 (2024), Issue 2 (Special issue: CIMPA schools "Nonassociative Algebras and related topics, Brazil'2023" and "Current Trends in Algebra, Philippines'2024") (October 26, 2023) cm:11514
We introduce the notions of alternating roots of polynomials and alternating polynomials over a Cayley-Dickson algebra, and prove a connection between the alternating roots of a given polynomial and the roots of the corresponding alternating polynomi
Externí odkaz:
http://arxiv.org/abs/2306.15889
Autor:
Reshetnyak, A., Moshin, P.
We deduce a non-linear commutator higher-spin (HS) symmetry algebra which encodes unitary irreducible representations of the AdS group -- subject to a Young tableaux $Y(s_1,\ldots ,s_k)$ with $k\geq 2$ rows -- in a $d$-dimensional anti-de-Sitter spac
Externí odkaz:
http://arxiv.org/abs/2305.00142
In this paper, we present some numerical applications for the equation $x^2+ax+b=0$, where $a, b$ are two quaternionic elements in $\mathbb{H}(\alpha,\beta)$. Based on well-known solving methods, we have developed a new numerical algorithm that solve
Externí odkaz:
http://arxiv.org/abs/2304.08930