Geometric Algebra and Grading

One of the most important aspects of geometric algebra is the grading. However, for many people, this is the first time they encounter the concept of grading, so they don't know the relevant definitions. In this short, I show these definitions, and how they imply that while geometric algebra is both an algebra and a graded space, it is not a graded algebra.

Also, I know that under the Z/2Z grading, GA is a graded algebra. However, we don't use that grading too much, and the N-grading is much more useful.

Patreon Supporters:
Christoph Kovacs
David Johnston
Jason Killian
p11
Richard Penner
Rosario
trb

[diribigal]

I asked "if we use the wedge product on that graded space, then we would have a graded algebra, right?" and sudgy clarified that "Yes, but that's the exterior algebra, not the geometric algebra".

[linuxp]

Can you make a short on complexified geometric algebras? How they differ from standard real algebras

[deltalima]

Where do tensors fall in? Are they bivectors?

[TheLethalDomain]

It's unfortunate that one of the most important parts of geometric algebra is "degrading." This saddens me deeply.