Topic
Quotient type
About: Quotient type is a research topic. Over the lifetime, 32 publications have been published within this topic receiving 358 citations.
Papers
TL;DR: In particular, the Poisson boundary and the quantum flag manifold are isomorphic for any q-deformed classical compact Lie group as discussed by the authors, and they are invariant under the left action of the dual discrete quantum group.
Abstract: Let \({\mathbb{G}}\) be a co-amenable compact quantum group. We show that a right coideal of \({\mathbb{G}}\) is of quotient type if and only if it is the range of a conditional expectation preserving the Haar state and is globally invariant under the left action of the dual discrete quantum group. We apply this result to the theory of Poisson boundaries introduced by Izumi for discrete quantum groups and generalize a work of Izumi-Neshveyev-Tuset on SUq(N) for co-amenable compact quantum groups with the commutative fusion rules. More precisely, we prove that the Poisson integral is an isomorphism between the Poisson boundary and the right coideal of quotient type by a maximal quantum subgroup of Kac type. In particular, the Poisson boundary and the quantum flag manifold are isomorphic for any q-deformed classical compact Lie group.
98 citations
TL;DR: In this paper, the authors classify Calabi-Yau threefold with infinite fundamental group by means of their minimal splitting coverings introduced by Beauville, and deduce that the nef cone is a rational simplicial cone and any rational nef divisor is semi-ample if the second Chern class is identically zero.
Abstract: First, we classify Calabi-Yau threefolds with infinite fundamental group by means of their minimal splitting coverings introduced by Beauville, and deduce that the nef cone is a rational simplicial cone and any rational nef divisor is semi-ample if the second Chern class is identically zero. We also derive a sufficient condition for the fundamental group to be finite in terms of the Picard number in an optimal form. Next, we give a concrete structure Theorem concerning $c_{2}$-contractions of Calabi-Yau threefolds as a generalisation and also a correction of our earlier works for simply connected ones. Finally, as an application, we show the finiteness of the isomorphism classes of $c_{2}$-contractions of each Calabi-Yau threefold.
79 citations
TL;DR: In particular, the Poisson boundary and the quantum flag manifold are isomorphic for any q-deformed classical compact Lie group as discussed by the authors, where q is the quantum subgroup of Kac type.
Abstract: Let $G$ be a co-amenable compact quantum group. We show that a right coideal of $G$ is of quotient type if and only if it is the range of a conditional expectation preserving the Haar state and is globally invariant under the left action of the dual discrete quantum group. We apply this result to theory of Poisson boundaries introduced by Izumi for discrete quantum groups and generalize a work of Izumi-Neshveyev-Tuset on $SU_q(N)$ for co-amenable compact quantum groups with the commutative fusion rules. More precisely, we prove that the Poisson integral is an isomorphism between the Poisson boundary and the right coideal of quotient type by maximal quantum subgroup of Kac type. In particular, the Poisson boundary and the quantum flag manifold are isomorphic for any q-deformed classical compact Lie group.
73 citations
TL;DR: In this paper, it was shown that the logarithmic Kodaira dimension of a normal surface defined over C is the same as the quotient dimension of the set of singularities of V.
Abstract: Let V be a normal surface defined over C. Following [3], we say V is logarithmic if all its singularities are of quotient type. It is called a Q-homology plane if its reduced homology groups with rational coefficients all vanish. Let J^ = {pi, ,pr} denote the set of singularities of V. Then recall that the logarithmic Kodaira dimension of V is defined to be the logarithmic Kodaira dimension of V \ ^ . In a sequence of three articles beginning with this, we propose to probe the following questions:
33 citations
Posted Content•
TL;DR: In this article, the authors classify Calabi-Yau threefold with infinite fundamental group by means of their minimal splitting coverings introduced by Beauville, and deduce that the nef cone is a rational simplicial cone and any rational nef divisor is semi-ample if the second Chern class is identically zero.
Abstract: First, we classify Calabi-Yau threefolds with infinite fundamental group by means of their minimal splitting coverings introduced by Beauville, and deduce that the nef cone is a rational simplicial cone and any rational nef divisor is semi-ample if the second Chern class is identically zero. We also derive a sufficient condition for the fundamental group to be finite in terms of the Picard number in an optimal form. Next, we give a concrete structure Theorem concerning $c_{2}$-contractions of Calabi-Yau threefolds as a generalisation and also a correction of our earlier works for simply connected ones. Finally, as an application, we show the finiteness of the isomorphism classes of $c_{2}$-contractions of each Calabi-Yau threefold.
29 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 5 |
| 2020 | 4 |
| 2019 | 3 |
| 2018 | 1 |
| 2017 | 1 |
| 2016 | 2 |