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1,003 results on '"Liu, Leilei"'

1. DG singular equivalence and singular locus

Author

Liu, Leilei and Zeng, Jieheng

Subjects
Mathematics - Commutative Algebra, Mathematics - Algebraic Geometry, Mathematics - Rings and Algebras, Mathematics - Representation Theory
Abstract

For a commutative Gorenstein Noetherian ring $R$, we construct an affine scheme $X$ solely from DG singularity category $S_{dg}(R)$ of $R$ such that there is a finite surjective morphism $X \rightarrow \mathrm{Spec}(R /I)$, where $\mathrm{Spec}(R /I)$ is the singular locus in $\mathrm{Spec}(R)$. As an application, for two such rings with equivalent DG singularity categories, we prove that the singular loci in their affine schemes have the same dimension., Comment: 18 pages

Published
2024

6. A Network Portrait Divergence Approach to Measure Science-Technology Linkages

Author

Meng, Kai, Ba, Zhichao, Liu, Leilei, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Bertino, Elisa, Editorial Board Member, Gao, Wen, Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Yung, Moti, Editorial Board Member, Sserwanga, Isaac, editor, Joho, Hideo, editor, Ma, Jie, editor, Hansen, Preben, editor, Wu, Dan, editor, Koizumi, Masanori, editor, and Gilliland, Anne J., editor

Published
2024
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28. Tilting objects in singularity categories of toric Gorenstein varieties

Author

Chen, Xiaojun, Liu, Leilei, and Zeng, Jieheng

Subjects
Mathematics - Algebraic Geometry, Mathematics - Rings and Algebras, Mathematics - Representation Theory
Abstract

We study certain toric Gorenstein varieties with isolated singularities which are the quotient spaces of generic unimodular representations by the one-dimensional torus, or by the product of the one-dimensional torus with a finite abelian group. Based on the works of \v{S}penko and Van den Bergh [Invent. Math. 210 (2017), no. 1, 3-67] and Mori and Ueyama [Adv. Math. 297 (2016), 54-92], we show that the singularity categories of these varieties admit tilting objects, and hence are triangle equivalent to the perfect categories of some finite dimensional algebras., Comment: 30 pages. Revised and title changed

Published
2021

29. Batalin-Vilkovisky algebra structure on Poisson manifolds with diagonalizable modular symmetry

Author

Chen, Xiaojun, Liu, Leilei, Yu, Sirui, and Zeng, Jieheng

Subjects
Mathematics - Differential Geometry, Mathematical Physics, 53D17, 55D05, 17B63
Abstract

We study the ``twisted" Poincar\'e duality of smooth Poisson manifolds, and show that, if the modular vector field is diagonalizable, then there is a mixed complex associated to the Poisson complex, which, combining with the twisted Poincar\'e duality, gives a Batalin-Vilkovisky algebra structure on the Poisson cohomology. This generalizes the previous results obtained by Xu for unimodular Poisson manifolds. We also show that the Batalin-Vilkovisky algebra structure is preserved under Kontsevich's deformation quantization, and in the case of polynomial algebras it is also preserved by Koszul duality., Comment: 30 pages

Published
2021

38. Twisted bi-symplectic structure on Koszul twisted Calabi-Yau algebras

Author

Chen, Xiaojun, Eshmatov, Alimjon, Eshmatov, Farkhod, and Liu, Leilei

Subjects
Mathematics - Rings and Algebras
Abstract

For a Koszul Artin-Schelter regular algebra (also called twisted Calabi-Yau algebra), we show that it has a "twisted" bi-symplectic structure, which may be viewed as a noncommutative and twisted analogue of the shifted symplectic structure introduced by Pantev, To\"en, Vaqui\'e and Vezzosi. This structure gives a quasi-isomorphism between the tangent complex and the twisted cotangent complex of the algebra, and may be viewed as a DG enhancement of Van den Bergh's noncommutative Poincar\'e duality; it also induces a twisted symplectic structure on its derived representation schemes., Comment: 27 pages

Published
2020

40. miR-141-3p accelerates ovarian cancer progression and promotes M2-like macrophage polarization by targeting the Keap1-Nrf2 pathway

Author

Zhao Jingyun, Liu Leilei, Zhao Wei, Lv Cuiting, Zhang Na, Jia Xinzhuan, and Zhang Zhengmao

Subjects
ovarian cancer, macrophage, polarization, mir-141-3p, keap1, nrf2, Medicine
Abstract

The miR-141-3p has been reported to participate in regulating autophagy and tumor-stroma interactions in ovarian cancer (OC). We aim to investigate whether miR-141-3p accelerates the progression of OC and its effect on macrophage 2 polarization by targeting the Kelch-like ECH-associated protein1-Nuclear factor E2-related factor2 (Keap1-Nrf2) pathway. SKOV3 and A2780 cells were transfected with miR-141-3p inhibitor and negative control to confirm the regulation of miR-141-3p on OC development. Moreover, the growth of tumors in xenograft nude mice treated by cells transfected with miR-141-3p inhibitor was established to further testify the role of miR-141-3p in OC. The expression of miR-141-3p was higher in OC tissue compared with non-cancerous tissue. Downregulation of miR-141-3p inhibited the proliferation, migration, and invasion of ovarian cells. Furthermore, miR-141-3p inhibition also suppressed M2-like macrophage polarization and in vivo OC progression. Inhibition of miR-141-3p significantly enhanced the expression of Keap1, the target gene of miR-141-3p, and thus downregulated Nrf2, while activation of Nrf2 reversed the reduction in M2 polarization by miR-141-3p inhibitor. Collectively, miR-141-3p contributes to tumor progression, migration, and M2 polarization of OC by activating the Keap1-Nrf2 pathway. Inhibition of miR-141-3p attenuates the malignant biological behavior of ovarian cells by inactivating the Keap1-Nrf2 pathway.

Published
2023
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