Homotopes of Symmetric Spaces I. Construction by Algebras with Two Involutions

TL;DR

This paper introduces a method to construct homotopes of classical symmetric spaces using associative algebras with involutions, revealing a duality between the space and deformation parameters.

Contribution

It provides an elementary construction of homotopes for symmetric spaces via associative algebras with multiple involutions, highlighting a novel duality.

Findings

Constructed homotopes of classical symmetric spaces.

Revealed a duality between space and deformation parameter.

Provided an elementary algebraic approach.

Abstract

We investigate a special kind of contraction of symmetric spaces (respectively, of Lie triple systems), called homotopy. In this first part of a series of two papers we construct such contractions for classical symmetric spaces in an elementary way by using associative algebras with several involutions. This construction shows a remarkable duality between the underlying "space" and the "deformation parameter".