Transitive partial actions of groups

Choi, Keunbae; Lim, Yongdo

doi:10.1007/s10998-008-6169-8

Cited by 9 publications

(9 citation statements)

References 11 publications

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“…A direct consequence of the last proposition is the following result ( [2], Proposition 2.5 and Theorem 2.6). …”

Section: (X α) Is Transitive If and Only If (T β) Is Transitivementioning

confidence: 73%

“…In a similar way the n-transitive partial actions are defined. In [2] was proved that (X, α) is transitive if and only if (T, β) is transitive (Proposition 2.4). This fact is a direct consequence of Theorem 5.…”

Section: Theorem 5 Let (X α) Be a Partial Action With Enveloping Acmentioning

confidence: 99%

“…In [2] the notion of a partial stabilizer was defined analogously to the global case and it was proved that this set is a subgroup of G (Proposition 2.5). However, in our case we follow a different path using enveloping actions.…”

Section: (X α) Is Transitive If and Only If (T β) Is Transitivementioning

confidence: 99%

“…Later in 2003, Abadie ([1]) introduced the notion of enveloping action and found that any partial action possesses an enveloping action. Many studies have shown that partial actions are a powerful tool to generalize many well-known results of global actions (see [2], [5] and the literature quoted therein).…”

Section: Introductionmentioning

confidence: 99%

“…In 2009, Choi and Lim ( [2]) introduced the concept of transitive partial action. Among other results, they proved that each transitive partial group action is the restriction of a group coset action.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

On Partial Orbits and Stabilizers

Ávila¹,

Hernández-González²,

Ortiz-Jara³

2014

Int. Elec. J. of Pure and Appl. Math.

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Within the framework of partial actions of groups, we introduce here the partial stabilizer and prove that it coincides with the global stabilizer. In addition, we define the partial orbits and show that they are completely determined by the global orbits. Finally, we use this result to prove that the partial action (X, α) is n − transitive if and only if its enveloping action (T, β) is n − transitive.

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“…A direct consequence of the last proposition is the following result ( [2], Proposition 2.5 and Theorem 2.6). …”

Section: (X α) Is Transitive If and Only If (T β) Is Transitivementioning

confidence: 73%

Section: Theorem 5 Let (X α) Be a Partial Action With Enveloping Acmentioning

confidence: 99%

Section: (X α) Is Transitive If and Only If (T β) Is Transitivementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

On Partial Orbits and Stabilizers

Ávila¹,

Hernández-González²,

Ortiz-Jara³

2014

Int. Elec. J. of Pure and Appl. Math.

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Partial group actions and partial Galois extensions

Kuo

Szeto

2016

Monatsh Math

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Recent developments around partial actions

Dokuchaev

2018

São Paulo J. Math. Sci.

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We give an overview of publications on partial actions and related concepts, paying main attention to some recent developments on diverse aspects of the theory, such as partial actions of semigroups, of Hopf algebras and groupoids, the globalization problem for partial actions, Morita theory of partial actions, twisted partial actions, partial projective representations and the Schur multiplier, cohomology theories related to partial actions, Galois theoretic results, ring theoretic properties and ideals of partial crossed products. Among the applications we consider in more detail the case of the Carlsen-Matsumoto C *-algebra related to an arbitrary subshift, but also mention many others. The total number of publications directly related to partial actions and partial representations is more than 130, so that it is impossible even to describe briefly the content of all of them within the constraints of the present survey. Thus, the majority of them are only cited with respects to specific topics, trying to give an idea about the involved matter. In order to complete the picture, we refer the reader to a recent book by Ruy Exel, to our previous surveys, as well as to those by other authors.

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Transitive partial actions of groups

Cited by 9 publications

References 11 publications

On Partial Orbits and Stabilizers

On Partial Orbits and Stabilizers

Partial group actions and partial Galois extensions

Recent developments around partial actions

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