Existence of Pseudo-Superinvolutions of the First Kind
Our main purpose is to develop the theory of existence of pseudo-superinvolutions of the first kind on finite dimensional central simple associative superalgebras over 𝐾, where 𝐾 is a field of characteristic not 2. We try to show which kind of finite dimensional central simple associative super...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2008-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/386468 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | Our main purpose is to develop the theory of existence of pseudo-superinvolutions of the first kind on finite dimensional central simple associative superalgebras over 𝐾, where 𝐾
is a field of characteristic not 2. We try to
show which kind of finite dimensional central simple associative superalgebras
have a pseudo-superinvolution of the first kind.
We will show that a division superalgebra 𝒟
over a field 𝐾
of characteristic not 2 of even type has pseudo-superinvolution (i.e., 𝐾-antiautomorphism 𝐽 such that (𝑑𝛿)𝐽2=(−1)𝛿𝑑𝛿)
of the first kind if and only if 𝒟
is of order 2 in the Brauer-Wall group BW(𝐾). We will also show that a division superalgebra 𝒟
of odd type over a field 𝐾
of characteristic not 2 has a pseudo-superinvolution of the first kind if and only if √−1∈𝐾,
and 𝒟
is of order 2 in the Brauer-Wall group BW(𝐾).
Finally, we study the existence of pseudo-superinvolutions on central simple superalgebras
𝒜=𝑀𝑝+𝑞(𝒟0). |
|---|---|
| ISSN: | 0161-1712 1687-0425 |