arXiv subjects

Daisuke Tambara

Publications and source records attributed to Daisuke Tambara.

3 recordsLinked to original sources

arXiv2026

The space of two-dimensional vectors over a four-dimensional division algebra over $F_2$

Let $A$ be a non-associative division algebra over a field $F$. Let $A$ act on the space $A^2$ by left multiplication. For nonzero elements $v, v'$ of $A^2$ we ask when the subspaces $Av$ and $Av'$ coincide. The paper gives an answer in the case where $A$ is four-dimensional and $F$ is the field of order 2. In this case $A$ is known to be isotopic to either of two algebras, system $V$ and system $W$ of Knuth. For each of these two algebras we give an explicit solution of the equation $Av=Av'$. The result is stated for any four-dimensional algebra $A$ defined over an arbitrary base field $F$ and equipped with the multiplication rule of system $V$ or system $W$.

math.RA↗

arXiv2024

Intersection of subspaces in $A^2$ for a three-dimensional division algebra $A$ over a finite field

Let $A$ be a three-dimensional nonassociative division algebra over a finite field. Let $A$ act on the space $A^2$ by left multiplication. For a nonzero vector $v$ in $A^2$ we have a three-dimensional subspace $Av$ in $A^2$. This paper concerns about possible dimension of the intersection of $Av$ and $Av'$ for $v, v'$ in $A^2$. One of our results is that there exists a two-dimensional intersection if and only if $A$ is isotopic to a commutative algebra. We use a classical theorem that A is a twisted field of Albert.

math.RA↗

arXiv1997

Quantum Galois theory for finite groups

We prove the Galois correspondence between the subgroups of a finite automorphism group G of a simple vertex operator algebra V and the vertex operator subalgebras of V containing the set V^G of G-invariants.

q-alg↗