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2019 |
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报告10 |
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题 目 |
New area-minimizing Lawson-Ossermann cones |
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报告人 |
许小卫（中国科学技术大学） |
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地 点 |
磬苑校区理工H楼401室 |
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时 间 |
2019年11月22日（周五）下午16:00-17:00 |
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摘 要 |
In this talk, I will introduce three types of Lawson-Osserman cones. They are compositions of a Hopf fibration and standard isometric minimal immersions of degree two. By using Lawlor's criterion, we show that they are area-minimizing. In particular, two undetermined minimal cones given in [LO77] will be shown area-minimizing. This is a joint work with Ling Yang and Yongsheng Zhang. |
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报 告9 |
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题 目 |
Howe duality for quantum queer superalgebra |
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报告人 |
汪永杰（合肥工业大学） |
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地 点 |
磬苑校区理工H楼401室 |
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时 间 |
2019年11月22日（周五）下午15:00-16:00 |
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摘 要 |
In this talk, we establish a new Howe duality between a pair of quantum queer superalgebras. The key ingredient is the construction of a non-commutative analogue $A_q(q_n, q_m)$ of the symmetric superalgebra S(C^{mn|mn}) with the use of quantum coordinate queer superalgebra. It turns out that this superalgebra is equipped with a $U_q^{−1} (q_n) \otimes U_q(q_m)$- supermodule structure that admits a multiplicity-free decomposition. We also show that the $(U_q^{−1} (q_n), U_q(q_m))$-Howe duality implies the Sergeev-Olshanski duality. This is my joint work with Z. Chang. |
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报 告8 |
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题 目 |
Tilting modules over Auslander Gorenstein algebras |
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报告人 |
张孝金副教授（南京信息工程大学） |
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地 点 |
磬苑校区数学楼H401室 |
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时 间 |
2019年5月11日（周六） 上午09:00-09:50 |
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摘 要 |
For a finite-dimensional algebra A and a
nonnegative integer n, we characterize when the set
tiltn A of additive equivalence classes of tilting
modules with projective dimension at most n has a
minimal (or equivalently, minimum) element. This generalizes
results of Happel and Unger. Moreover, for an n-Gorenstein
algebra A with n\ge
1, we construct a minimal element in tiltn A. As a
result, we give equivalent conditions for a k-Gorenstein
algebra to be Iwanaga–Gorenstein. Moreover, for a 1-Gorenstein
algebra A and its factor algebra B=A/(e),
we show that there is a bijection between tilt1A
and the set st-tilt B of additive equivalence
classes of basic support tau-tilting B-modules, where
e is an idempotent such that eA is the additive
generator of the category of projective-injective A
-modules. |
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报 告7 |
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题 目 |
Recollements, comma categories and morphic
enhancements |
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报告人 |
陈小伍教授（中国科学技术大学） |
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地 点 |
磬苑校区数学楼H401室 |
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时 间 |
2019年5月11日（周六） 上午10:00-10:50 |
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摘 要 |
We relate a recollement of triangulated categories to a
certain comma category. For a morphic enhancement in the
sense of Keller, we obtain three functors, which relate the
enhanced triangulated category to the module category over
the given triangulated category. This extends the work by
Ringel-Zhang (2014) and Eiriksson (2017). |
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报 告6 |
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题 目 |
The Extension Dimensions of Abelian Categories |
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报告人 |
黄兆泳教授（南京大学） |
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地 点 |
磬苑校区数学楼H401室 |
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时 间 |
2019年5月11日（周六） 上午11:00-11:50 |
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摘 要 |
Let $\mathcal{A}$ be an abelian category having enough
projective objects and enough injective objects. We prove
that if $\mathcal{A}$ admits an additive generating object,
then the extension dimension and the weak resolution
dimension of $\mathcal{A}$ are identical, and they are at
most the representation dimension of $\mathcal{A}$ minus
two. By using it, for a right Morita ring $\Lambda$, we
establish the relation between the extension dimension of
the category mod-$\Lambda$ of finitely generated right
$\Lambda$-modules and the representation dimension as well
as the global dimension of $\Lambda$. In particular, we give
an upper bound for the extension dimension of mod-$\Lambda$
in terms of the projective dimension of certain class of
simple right $\Lambda$-modules and the radical layer length
of $\Lambda$. In addition, we investigate the behavior of
the extension dimension under some ring extensions.
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报 告5 |
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目 |
PBW-deformations of type $\mathbb{A}_n$ quantum groups via multiple Ore
extensionses
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| 报告人 |
王顶国教授（曲阜师范大学） |
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时 间 |
2019年4月29日（周一）下午15:00-16:00 |
| 地 点 |
磬苑校区数学楼H306室 |
| 摘 要 |
The notion of multiple Ore
extension is introduced as a natural generalization of Ore
extensions and double Ore extensions.
For a PBW-deformation $\mathcal{B}_q(\mathfrak{sl}(n+1,
\mathbb{C}))$ of
type $\mathbb {A}_n$ quantum group, we explicitly obtain the
commutation relations of its root vectors,
then show that it can be realized via a series of
multiple Ore extensions, which we call a ladder Ore extension of
type $(1, 2, \cdots, n)$.
Moreover, we analyze the quantum algebras $\mathcal{B}_q(\mathfrak{g})$
of type $\mathbb {D}_4$, $\mathbb{B}_2$ and $\mathbb{G}_2$ and
give some examples and counterexamples that can be realized by a
ladder Ore extension. This is based on a joint work with Yongjun
Xu and Hualin Huang. |
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报 告4 |
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目 |
The prime spectrum of the algebra $\mathbb{K}_q[X, Y] \rtimes
U_q(sl_2)$ and
a classification of simple weight modules
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| 报告人 |
陆涛博士 (华侨大学) |
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时 间 |
2019年4月18日（周四）下午16:00-17:00 |
| 地 点 |
磬苑校区数学楼H306室 |
| 摘 要 |
For the algebra A in the title, it
is shown that its centre is generated by an explicit quartic
element. Explicit descriptions are given of the prime,
primitive and maximal spectra of the algebra A. A
classification of simple weight A-modules is obtained. |
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| 报 告3 |
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| 题
目 |
The
global dimension of the algebras of polynomial integro-differential
operators
and the
Jacobian algebras.
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| 报告人 |
Vladimir
V. Bavula教授 (谢菲尔德大学，英国) |
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时 间 |
2019年4月18日（周四）下午15:00-16:00 |
| 地 点 |
磬苑校区数学楼H306室 |
| 摘 要 |
We discuss homological properties of the algebras of polynomial integro-differential
operators, the Jacobian algebras and their factor algebras.
In particular, their global and weak homological dimensions
are found. |
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| 报 告2 |
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| 题
目 |
Koszul代数简介 |
| 报告人 |
叶郁教授 (中国科学技术大学) |
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时 间 |
2019年4月16日（周二）下午15:00-16:00 |
| 地 点 |
磬苑校区数学楼H401室 |
| 摘 要 |
我们将对Koszul代数作一个简单回顾，包括Koszul代数和Koszul对偶的基本概念和性质，Koszul代数的一些常用判别方法和构造等。此外，我们将介绍我们对二次超曲面的一些最新认识和相关的一些最近进展。 |
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| 报 告1 |
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| 题
目 |
Pointed finite tensor categories over finite abelian groups |
| 报告人 |
黄华林教授（华侨大学） |
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时 间 |
2019.3.25（周一） 上午10：30-11：30 |
| 地 点 |
安徽大学磬苑校区H306报告厅 |
| 摘 要 |
We will report some results on constructions and classifications
of finite quasi-quantum groups over finite abelian groups. The
talk is based on a series of recent joint works with Gongxiang
Liu, Yuping Yang and Yu Ye. |
