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...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/386468 |
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| author | Ameer Jaber |
| author_facet | Ameer Jaber |
| author_sort | Ameer Jaber |
| collection | DOAJ |
| description | 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). |
| format | Article |
| id | doaj-art-0cee6ace2401481c914f5f6e03a11ee3 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-0cee6ace2401481c914f5f6e03a11ee32025-02-03T05:50:08ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/386468386468Existence of Pseudo-Superinvolutions of the First KindAmeer Jaber0Department of Mathematics, The Hashemite University, Zarqa 13115, JordanOur 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).http://dx.doi.org/10.1155/2008/386468 |
| spellingShingle | Ameer Jaber Existence of Pseudo-Superinvolutions of the First Kind International Journal of Mathematics and Mathematical Sciences |
| title | Existence of Pseudo-Superinvolutions of the First Kind |
| title_full | Existence of Pseudo-Superinvolutions of the First Kind |
| title_fullStr | Existence of Pseudo-Superinvolutions of the First Kind |
| title_full_unstemmed | Existence of Pseudo-Superinvolutions of the First Kind |
| title_short | Existence of Pseudo-Superinvolutions of the First Kind |
| title_sort | existence of pseudo superinvolutions of the first kind |
| url | http://dx.doi.org/10.1155/2008/386468 |
| work_keys_str_mv | AT ameerjaber existenceofpseudosuperinvolutionsofthefirstkind |