The product of an involution and a skew-involution

Paras, Agnes T.; Salinasan, Jenny R.

doi:10.1016/j.laa.2019.09.035

Cited by 1 publication

(4 citation statements)

References 3 publications

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“…and B is similar to −B −1 then, by the Theorem 5 in [5], B is product of one involution S and one skew-involution T . Then we have…”

Section: ) a Is A Product Of Commutators Of One Skew-involution And O...mentioning

confidence: 92%

“…Paras and Salinasan in [5] shows the necessary and sufficient condition for a matrix A over a field to be the product of an involution and a skew-involution. In the section 4, the authors give a necessary and sufficient condition for every matrix in SL n (C) to be written as product of commutators of one involution and one skew-involution.…”

Section: ) Two Commutators Of Skew-involutions and Involutions Both I...mentioning

confidence: 99%

“…In case of product of comutators we can see [5,8,9]. Also in [5] the author shows the necessary and sufficient condition for a matrix over a field to be the product of an involution and a skew-involution.…”

Section: Introductionmentioning

confidence: 99%

“…For example, expressing matrices as a product of involutions was studied by several authors [6,7,11,12]. In case of product of comutators we can see [5,8,9]. Also in [5] the author shows the necessary and sufficient condition for a matrix over a field to be the product of an involution and a skew-involution.…”

Section: Introductionmentioning

confidence: 99%

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Expressing Matrices Into Products of Commutators of Involutions, Skew-Involutions, Finite Order and Skew Finite Order Matrices

Gargate,

Gargate

2020

Preprint

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Let R be an associative ring with unity 1 and consider that 2, k and 2k ∈ N are invertible in R. For m ≥ 1 denote by U Tn(m, R) and U T∞(m, R), the subgroups of U Tn(R) and U T∞(R) respectively, which have zero entries on the first m − 1 super diagonals. We show that every element on the groups U Tn(m, R) and U T∞(m, R) can be expressed as a product of two commutators of involutions and also, can be expressed as a product of two commutators of skew-involutions and involutions in U T∞(m, R). Similarly, denote by U T (s) ∞ (R) the group of upper triangular infinite matrices whose diagonal entries are sth roots of 1. We show that every element of the groups U Tn(∞, R) and U T∞(m, R) can be expressed as a product of 4k − 6 commutators all depending of powers of elements in U T (k) ∞ (m, R) of order k and, also, can be expressed as a product of 8k − 6 commutators of skew finite matrices of order 2k and matrices of order 2k in U T (2k) ∞ (m, R). If R is the complex field or the real number field we prove that, in SLn(R) and in the subgroup SL V K (∞, R) of the Vershik-Kerov group over R, each element in these groups can be decomposed into a product of commutators of elements as described above.

show abstract

“…and B is similar to −B −1 then, by the Theorem 5 in [5], B is product of one involution S and one skew-involution T . Then we have…”

Section: ) a Is A Product Of Commutators Of One Skew-involution And O...mentioning

confidence: 92%

Section: ) Two Commutators Of Skew-involutions and Involutions Both I...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Expressing Matrices Into Products of Commutators of Involutions, Skew-Involutions, Finite Order and Skew Finite Order Matrices

Gargate,

Gargate

2020

Preprint

View full text Add to dashboard Cite

show abstract

The product of an involution and a skew-involution

Cited by 1 publication

References 3 publications

Expressing Matrices Into Products of Commutators of Involutions, Skew-Involutions, Finite Order and Skew Finite Order Matrices

Expressing Matrices Into Products of Commutators of Involutions, Skew-Involutions, Finite Order and Skew Finite Order Matrices

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