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On Rees algebras and invariants for singularities over perfect fields
Rees algebras Integral closure Singularities Commutative Algebra
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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...
Cayley-Dickson and Clifford Algebras as Twisted Group Algebras
twisted group algebra sign function Cayley-Dickson algebra Clifford algebra quaternions octonions
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2011/8/26
Abstract: The effect of some properties of twisted groups on the associated algebras, particularly Cayley-Dickson and Clifford algebras. It is conjectured that the Hilbert space of square-summable seq...
Properly twisted groups and their algebras
twisted group algebra Cayley-Dickson algebra Clifford algebra quaternions octonions
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2011/8/26
Abstract: A twist property is developed which imparts certain properties on the twisted group algebra. These include an involution * satisfying (xy)*=y*x* and an inner product satisfying =
Pfaffian quartic surfaces and representations of Clifford algebras
Pfaffian quartic surfaces representations of Clifford algebras Algebraic Geometry Rings and Algebras
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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
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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...
On extensions of Lie algebras
extensions of Lie algebras Rings and Algebras
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2011/8/29
Abstract: In the note some construction of Lie algebras is introduced. It is proved that the construction has the same property as a well known wreath product of groups [1]: Any extension of groups ca...
On resolutions of diagrams of algebras
diagrams of algebras Algebraic Topology K-Theory and Homology
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2011/8/29
Abstract: We prove a restricted version of a conjecture by M. Markl on resolutions of an operad describing diagrams of algebras. We discuss a particular case related to the Gerstenhaber-Schack diagram...
On stably free modules over affine algebras
stably free modules affine algebras Grothendieck-Witt groups symplectic Witt groups
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2011/8/25
Abstract: We prove that stably free modules of rank d-1 over a smooth affine algebra of dimension d over an algebraically closed field k are free, provided (d-1)! is nonzero in k.
Exel and Stacey crossed products, and Cuntz-Pimsner algebras
Exel crossed product Stacey crossed product Cuntz-Pimsner algebra endomorphism
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2011/8/25
Abstract: There are many different crossed products by an endomorphism of a C*-algebra, and constructions by Exel and Stacey have proved particularly useful. Here we show that every Exel crossed produ...
Integral Bases for the Universal Enveloping Algebras of Map Algebras
the Universal Enveloping Algebras Map Algebras Integral Bases Representation Theory
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2011/8/26
Abstract: Given a finite-dimensional, complex simple Lie algebra we exhibit an integral form for the universal enveloping algebra of its map algebra, and an explicit integral basis for this integral f...
Solution algebras of differential equations and quasi-homogeneous varieties
solution algebra differential algebra differential Galois group observable subgroup geometric invariant theory quasi-homogeneous variety
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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...
Poisson algebras and Jacobi pairs
Poisson algebras Jacobian conjecture Jacobi pairs
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2011/8/26
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...
Gradings on walled Brauer algebras and Khovanov's arc algebra
walled Brauer algebras Khovanov's arc algebra Gradings
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2011/8/25
Abstract: We introduce some graded versions of the walled Brauer algebra, working over a field of characteristic zero. This allows us to prove that the walled Brauer algebra is Morita equivalent to an...
The Douglas property for multiplier algebras of operators
corona theorem, reproducing kernels Functional Analysis
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2011/8/25
Abstract: For a collection of reproducing kernels k which includes those for the Hardy space of the polydisk and ball and for the Bergman space, k is a complete Pick kernel if and only if the multipli...
Lie algebras and Yang-Baxter equations
Lie algebras Yang-Baxter equations Quantum Algebra
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2011/8/25
Abstract: At the previous congress (CRM 6), we reviewed the construction of Yang-Baxter operators from associative algebras, and presented some (colored) bialgebras and Yang-Baxter systems related to ...