The J-invariant and Tits algebras for groups of inner type E6

TL;DR

This paper extends the connection between Tits algebra indices and the motivic J-invariant for groups of inner type E6 by incorporating higher Chern class maps, offering new insights into algebraic group invariants.

Contribution

It generalizes previous results by including higher Chern class maps and applies these findings specifically to groups of inner type E6.

Findings

Extended the link between Tits algebra indices and the J-invariant using higher Chern classes.

Provided new applications to algebraic groups of inner type E6.

Enhanced understanding of motivic invariants in algebraic group theory.

Abstract

A connection between the indices of the Tits algebras of a split linear algebraic group G and the degree one parameters of its motivic J-invariant was introduced by Queguiner-Mathieu, Semenov and Zainoulline through use of the second Chern class map in the Riemann-Roch theorem without denominators. In this paper we extend their result to higher Chern class maps and provide applications to groups of inner type E6.