Involutions of Type G2 Over Fields of Characteristic Two

Hutchens, John; Schwartz, Nathaniel

doi:10.1007/s10468-017-9723-y

Cited by 4 publications

(5 citation statements)

References 27 publications

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“…In particular we want to extend Helminck's study of k-involutions and symmetric k-varieties [15] to include fields of characteristic 2. This has been studied for groups of type G 2 and A n in [22,25] and over fields of characteristic not 2 in [6,3,2,4,19,20,21]. We also extend the results of Aschbacher and Seitz [1] who studied similar structures for finite fields of characteristic 2.…”

Section: Introductionsupporting

confidence: 63%

“…Over fields of characteristic not 2 the G(k)-conjugacy classes of automorphisms of order 2 are in bijection with G(k)-conjugacy classes of fixed point groups of involutions on G as seen in [16]. However, in characteristic 2 there are examples of involutions that are not G(k)-conjugate with isomorphic fixed point groups, see Theorem 5.23, as well as Theorem 5.27 in [22].…”

Section: Introductionmentioning

confidence: 99%

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Fixed point groups of involutions of type $\mathrm{O}(\mathrm{q},k)$ over a field of characteristic two

Hunnell¹,

Hutchens²

2023

Preprint

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For O(q, k), the orthogonal group over a field k of characteristic 2 with respect to a quadratic form q, we discuss the isomorphism classes of fixed points of involutions. When the quadratic space is either totally singular or nonsingular, a full classification of the isomorphism classes is given. We also give some implications of these results for a general quadratic space over a field of characteristic 2.

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Section: Introductionsupporting

confidence: 63%

Section: Introductionmentioning

confidence: 99%

Fixed point groups of involutions of type $\mathrm{O}(\mathrm{q},k)$ over a field of characteristic two

Hunnell¹,

Hutchens²

2023

Preprint

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show abstract

“…The primary motivation is to extend Helminck's [14] study of k-involutions and symmetric k-varieties to include fields of characterstic 2. This has been studied for groups of type G 2 and A n in [19,22] and over fields of characteristic not 2 in [6,3,2,4,16,17,18]. We also extend the results of Aschbacher and Seitz [1] who studied similar structures for finite fields of characteristic 2.…”

Section: Introductionsupporting

confidence: 63%

On involutions of type O(q,k) over a field of characteristic two

Hunnell

Hutchens

Schwartz³

2020

Linear Algebra and its Applications

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“…We would like to correct two errors in our paper Involutions of type G 2 over a field of characteristic 2 [2]. The errors relate to the discussions and results of involutons of type I in Sections 3 and 4, and specifically to Lemma 3.3, Lemma 4.8, Proposition 4.10, Theorem 4.11 and Lemma 4.12.…”

mentioning

confidence: 99%

“…If an involution t ∈ Aut(C) fixes a four dimensional totally singular subalgebra we call it an involution of type II. This case is discussed in Section 5 of [2].…”

mentioning

confidence: 99%