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Differential identities of matrix algebras

Autor: Brox, Jose, Rizzo, Carla

We study the differential identities of the algebra $M_k(F)$ of $k\times k$ matrices over a field $F$ of characteristic zero when its full Lie algebra of derivations, $L=\mbox{Der}(M_k(F))$, acts on it. We determine a set of 2 generators of the ideal

Externí odkaz: http://arxiv.org/abs/2403.09337

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Weak representability of actions of non-associative algebras

Autor: Brox, Jose, García-Martínez, Xabier, Mancini, Manuel, Van der Linden, Tim, Vienne, Corentin

We study the categorical-algebraic condition that internal actions are weakly representable (WRA) in the context of varieties of (non-associative) algebras over a field. Our first aim is to give a complete characterization of action accessible, opera

Externí odkaz: http://arxiv.org/abs/2306.02812

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The determinant, spectral properties, and inverse of a tridiagonal $k$-Toeplitz matrix over a commutative ring

Autor: Brox, Jose, Albuquerque, Helena

A square matrix is $k$-Toeplitz if its diagonals are periodic sequences of period $k$. We find universal formulas for the determinant, the characteristic polynomial, some eigenvectors, and the entries of the inverse of any tridiagonal $k$-Toeplitz ma

Externí odkaz: http://arxiv.org/abs/2106.13157

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There are no nontrivial two-sided multiplicative (generalized)-skew derivations in prime rings

Autor: Brox, Jose

As originally defined by Ashraf and Mozumder, multiplicative (generalized)-skew derivations must satisfy two identities. In this short note we show that, as a consequence of the simultaneous satisfaction of both identities, a multiplicative (generali

Externí odkaz: http://arxiv.org/abs/2007.08013

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Higher polynomial identities for mutations of associative algebras

Autor: Bremner, Murray R., Brox, Jose, Sánchez-Ortega, Juana

We study polynomial identities satisfied by the mutation product $xpy - yqx$ on the underlying vector space of an associative algebra $A$, where $p, q$ are fixed elements of $A$. We simplify known results for identities in degree $4$, proving that on

Externí odkaz: http://arxiv.org/abs/1812.05481

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