Searcharxiv⌕ Search

arXiv subjects

Ricardo Suarez

Publications and source records attributed to Ricardo Suarez.

4 recordsLinked to original sources
arXiv2025

Complex tori constructed from Cayley-Dickson algebras

In this paper we construct complex tori, denoted by $S_{\mathbb{B}_{1,p,q}}$, as quotients of tensor products of Cayley--Dickson algebras, denoted $\mathbb{B}_{1,p,q}=\mathbb{C}\otimes \mathbb{H}^{\otimes p}\otimes \mathbb{O}^{\otimes q}$, with their integral subrings. We then show that these complex tori have endomorphism rings of full rank and are isogenous to the direct sum of $2^{2p+3q}$ copies of an elliptic curve $E$ of $j$-invariant $1728$.

math.AG↗
arXiv2025

Clifford Multiplication on Spinor Abelian Varieties

We define a spinor Abelian variety $S_{\Delta}$ to be a complex Abelian variety whose tangent space at the origin is a space of spinors for a suitable complex Clifford algebra $\mathbb{C}_{q}(V)$. We examine intrinsic properties of such varieties and the connection between Clifford multiplication and their endomorphism algebras. We then extend the analysis of Clifford multiplication to the dual torus $Pic^{0}(S_{\Delta})$.

math.AG↗
arXiv2019

Expository paper on Clifford algebras ,representations , and the octonion algebra

This paper is meant to be an informative introduction to spinor representations of Clifford algebras. In this paper we will have a look at Clifford algebras and the octonion algebra. We begin the paper looking at the quaternion algebra $\mathbb{H}$ and basic properties that relate Clifford algebras and the well know Pin and Spin groups. We then will look at generalized spinor representations of Clifford algebras, along with many examples. We conclude the paper looking at the octonion algebra $\mathbb{O}$. This paper provides background to constructing representations which can be used to look at elements in the appropriate Pin and Spin groups.

math.RT↗