Extensors

• Sep 29th 2009, 01:12 AM
TwistedOne151
Extensors
I'm familiar with tensors, but I recently encountered in a physics paper the term "extensor" (specifically, the "metric extensor" as constrasted with the metric tensor). What is an extensor? Can anyone point me to a definition or introduction to this term/concept/entity?

--Kevin C.
• Sep 29th 2009, 02:52 AM
NonCommAlg
Quote:

Originally Posted by TwistedOne151
I'm familiar with tensors, but I recently encountered in a physics paper the term "extensor" (specifically, the "metric extensor" as constrasted with the metric tensor). What is an extensor? Can anyone point me to a definition or introduction to this term/concept/entity?

--Kevin C.

let $\displaystyle V$ be a vector space over a field $\displaystyle F$ (or more generally a module over a commutative ring). let $\displaystyle \Lambda(V)$ be the exterior algebra of $\displaystyle V$ over $\displaystyle F.$ an extensor of step $\displaystyle n$ is any element of $\displaystyle \Lambda(V)$

in the form $\displaystyle v_1 \wedge v_2 \wedge \cdots \wedge v_n, \ \ v_j \in V.$