Rigid dualizing complexes over quantum homogeneous spaces

Liu, L.-Y.; Wu, Q.-S.

doi:10.1016/j.jalgebra.2011.12.007

Cited by 10 publications

(7 citation statements)

References 27 publications

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“…Many classes of algebras arising from noncommutative algebraic geometry or quantum group are twisted Calabi-Yau. We refer to [6], [7], [11], [16], [25], [29], [38], [40] and the references therein for more information and in particular plenty of examples. (1) In (4.2), the second variable A e in the Ext group has left and right A e -module structures.…”

Section: Nakayama Automorphismsmentioning

confidence: 99%

On homological smoothness of generalized Weyl algebras over polynomial algebras in two variables

Liu

2017

Preprint

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Section: Nakayama Automorphismsmentioning

confidence: 99%

On homological smoothness of generalized Weyl algebras over polynomial algebras in two variables

Liu

2017

Preprint

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“…(1) That T is homologically smooth follows from [24,Lemma 3.7]. Given that T is AS-regular by Theorem 4.3(4), [24,Theorem 3.6] implies that T is νtwisted Calabi-Yau , with ν = S 2 • τ ℓ χ . (2) Let T be a left coideal subalgebra of H := (H, µ, ∆, S, ǫ).…”

Section: 3mentioning

confidence: 99%

“…For the unexplained terminology in (3), see §4.3. The determination of the Nakayama automorphism in (3) depends crucially on earlier work of Kraehmer [18] and of Liu and Wu [23], [24].…”

Section: Introductionmentioning

confidence: 99%

Quantum homogeneous spaces of connected Hopf algebras

Brown

Gilmartin

2016

Journal of Algebra

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Let H be a connected Hopf k-algebra of finite Gel'fand-Kirillov dimension over an algebraically closed field k of characteristic 0. The objects of study in this paper are the left or right coideal subalgebras T of H. They are shown to be deformations of commutative polynomial k-algebras. A number of well-known homological and other properties follow immediately from this fact. Further properties are described, examples are considered, invariants are constructed and a number of open questions are listed.

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“…in [2,7,11,[14][15][16][17][18][19]21] generalise affine varieties with a transitive action of an algebraic group: Definition A quantum homogeneous space is a right coideal subalgebra B of a Hopf algebra A which is faithfully flat as a left B-module.…”

Section: Introductionmentioning

confidence: 99%

The Nodal Cubic is a Quantum Homogeneous Space

Krähmer

Tabiri

2017

Algebr Represent Theor

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The cusp was recently shown to admit the structure of a quantum homogeneous space, that is, its coordinate ring B can be embedded as a right coideal subalgebra into a Hopf algebra A such that A is faithfully flat as a B-module. In the present article such a Hopf algebra A is constructed for the coordinate ring B of the nodal cubic, thus further motivating the question which affine varieties are quantum homogeneous spaces.Keywords Hopf algebra · Quantum homogeneous space · Singular curve · Noncommutative Galois extension Mathematics Subject Classification (2010) 16T05 · 16T20 · 14H50 Just as quantum groups (Hopf algebras) generalise affine algebraic groups, quantum homogeneous spaces as studied e.g. in [2,7,11,[14][15][16][17][18][19]21] generalise affine varieties with a transitive action of an algebraic group: Definition A quantum homogeneous space is a right coideal subalgebra B of a Hopf algebra A which is faithfully flat as a left B-module.There is also an analytic theory of transitive or more generally ergodic actions of compact or locally compact quantum groups, see e.g. [8,13] and the references therein.

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Rigid dualizing complexes over quantum homogeneous spaces

Cited by 10 publications

References 27 publications

On homological smoothness of generalized Weyl algebras over polynomial algebras in two variables

On homological smoothness of generalized Weyl algebras over polynomial algebras in two variables

Quantum homogeneous spaces of connected Hopf algebras

The Nodal Cubic is a Quantum Homogeneous Space

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