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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The Cohen-Macaulay Auslander algebra of string algebras
串代数 Cohen—Macaulay—Auslander代数 拓扑 同调
2023/11/13
In these two talks, some results on derived representation type via topological and homological methods will be introduced: (1) Two geometric models for graded skew-gentle algebras will be introduced ...
Our aim here is to give a fairly self-contained exposition of some basic facts
about the Iwahori-Hecke algebra H of a split p-adic group G, including Bernstein’s
presentation and description of the ...
A NOTE ON STRONGLY SEPARABLE ALGEBRAS
Separable algebras invariants coinvariants coalgebras Hopf algebras
2015/8/14
Let A be an algebra over a field k. If M is an A–bimodule, we let
MA and MA denote respectively the k–spaces of invariants and coinvariants of
M, and 'M : MA
! MA be the natural map. In this note w...
QUADRI-ALGEBRAS
quadri-algebra operad Koszul duality
2015/8/14
We introduce the notion of quadri-algebras. These are associative algebras
for which the multiplication can be decomposed as the sum of four operations
in a certain coherent manner. We present sever...
On Rees algebras and invariants for singularities over perfect fields
Rees algebras Integral closure Singularities Commutative Algebra
2011/8/31
Abstract: This purpose of this paper is to show how Rees algebras can be applied in the study of singularities embedded in smooth schemes over perfect fields. In particular, we will study situations i...
Pfaffian quartic surfaces and representations of Clifford algebras
Pfaffian quartic surfaces representations of Clifford algebras Algebraic Geometry Rings and Algebras
2011/8/29
Abstract: Given a nondegenerate ternary form $f=f(x_1,x_2,x_3)$ of degree 4 over an algebraically closed field of characteristic zero, we use the geometry of K3 surfaces and van den Bergh's correspond...
On representations of Clifford algebras of ternary cubic forms
Clifford algebras ternary cubic forms Algebraic Geometry
2011/8/29
Abstract: In this article, we provide an overview of a one-to-one correspondence between representations of the generalized Clifford algebra $C_f$ of a ternary cubic form $f$ and certain vector bundle...
Solution algebras of differential equations and quasi-homogeneous varieties
solution algebra differential algebra differential Galois group observable subgroup geometric invariant theory quasi-homogeneous variety
2011/8/26
Abstract: We develop a new connection between Differential Algebra and Geometric Invariant Theory, based on an anti-equivalence of categories between solution algebras associated to a linear different...
Abstract: We define a Poisson algebra structure $(P,[\cdot,\cdot],\cdot)$ on the space $P:=\C[y]((x^{\frac1N}))$, and study its properties. In particular, we introduce some automorphisms of $(P,[\cdot...
A remarkable contraction of semisimple Lie algebras
Inonu-Wigner contraction coadjoint representation algebra of invariants orbit
2011/8/25
Abstract: Recently, E.Feigin introduced a very interesting contraction $\mathfrak q$ of a semisimple Lie algebra $\mathfrak g$ (see arXiv:1007.0646 and arXiv:1101.1898). We prove that these non-reduct...
Bilinear complexity of algebras and the Chudnovsky-Chudnovsky interpolation method
Bilinear complexity of algebras Chudnovsky-Chudnovsky interpolation method Computational Complexity
2011/9/29
Abstract: We give new improvements to the Chudnovsky-Chudnovsky method that provides upper bounds on the bilinear complexity of multiplication in extensions of finite fields through interpolation on a...
Geometric characterizations of the representation type of hereditary algebras and of canonical algebras
Canonical algebras exceptional sequences moduli spaces rational invariants
2010/12/8
We show that a finite connected quiver Q with no oriented cycles is tame if and only if for each dimension vector d and each integral weight of Q, the moduli space M(Q.
On geometric realizations of quantum modified algebras and their canonical bases, II
Quantum modified algebras canonical bases equivariant derived categories
2010/11/30
We prove part of the conjectures in [Li10a]. We also relate the construction of quantum modified algebras in [Li10a] with the functorial construction in [ZH08].