Anonymous
6/15/2025, 12:20:42 AM
No.16697979
>>16697958
Intro to Smooth Manifolds by Lee. That’s if you want to do tensor fields. Chapter 12 specifically. But tensors from an abstract point of view are just multilinear maps and tensor algebra is just a free algebra with vector spaces acting as generating sets. For that, something like Artin’s Algebra suffices. He covers free groups and polynomial rings (which are free objects in the category of groups and commutative rings respectively), so you can easily generalize to tensor algebras. Algebras have “ring like” behavior with ideals etc.
Intro to Smooth Manifolds by Lee. That’s if you want to do tensor fields. Chapter 12 specifically. But tensors from an abstract point of view are just multilinear maps and tensor algebra is just a free algebra with vector spaces acting as generating sets. For that, something like Artin’s Algebra suffices. He covers free groups and polynomial rings (which are free objects in the category of groups and commutative rings respectively), so you can easily generalize to tensor algebras. Algebras have “ring like” behavior with ideals etc.