The Structure Theorem of Weak Comodule Algebras

Zhang, Liangyun

doi:10.1080/00927870902865894

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Rota-baxter Leibniz Algebras1

Now We Will Construct Functors Connecting1

End H a (A H)#h ∼ = End A (A H)1

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Cited by 11 publications

(7 citation statements)

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“…Then, according to Corollary 2.2 (1) in [28], we know that Π is idempotent. Furthermore, if is commutative, then, by Corollary 2.2 (4) in [28], Π is also an algebra map. So…”

Section: Rota-baxter Leibniz Algebrasmentioning

confidence: 96%

Rota-Baxter Leibniz Algebras and Their Constructions

Zhang

Zheng

2018

Advances in Mathematical Physics

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In this paper, we introduce the concept of Rota-Baxter Leibniz algebras and explore two characterizations of Rota-Baxter Leibniz algebras. And we construct a number of Rota-Baxter Leibniz algebras from Leibniz algebras and associative algebras and discover some Rota-Baxter Leibniz algebras from augmented algebra, bialgebra, and weak Hopf algebra. In the end, we give all Rota-Baxter operators of weight 0 and -1 on solvable and nilpotent Leibniz algebras of dimension ≤3, respectively.

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“…Then, according to Corollary 2.2 (1) in [28], we know that Π is idempotent. Furthermore, if is commutative, then, by Corollary 2.2 (4) in [28], Π is also an algebra map. So…”

Section: Rota-baxter Leibniz Algebrasmentioning

confidence: 96%

Rota-Baxter Leibniz Algebras and Their Constructions

Zhang

Zheng

2018

Advances in Mathematical Physics

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“…for all a, b ∈ A and v ∈ V . In particular, for 11) for all a, b, a ∈ A. We will first prove that the adjunction map…”

Section: Now We Will Construct Functors Connectingmentioning

confidence: 98%

The Affineness Criterion for Weak Yetter-Drinfel’d Modules

Guo¹

2014

International Electronic Journal of Algebra

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“…3), we obtain the structure theorem for weak comodule algebras given in [24]: there exists an algebra isomorphism as follows: …”

Section: End H a (A H)#h ∼ = End A (A H)mentioning

confidence: 99%

“…By[24], if there exists a right H-comodule algebra map γ :H −→ A, then A is in H M H A ,where the left and right actions of A are given by h ≻ a = γ (h)a and its multiplication, respectively. So, by (1), Theorem 2.7(2) and Lemma 2.4(…”

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confidence: 99%