1,773 research outputs found
Classification of Reductive Monoid Spaces Over an Arbitrary Field
In this semi-expository paper we review the notion of a spherical space. In
particular we present some recent results of Wedhorn on the classification of
spherical spaces over arbitrary fields. As an application, we introduce and
classify reductive monoid spaces over an arbitrary field.Comment: This is the final versio
Additive combinatorics methods in associative algebras
We adapt methods coming from additive combinatorics in groups to the study of
linear span in associative unital algebras. In particular, we establish for
these algebras analogues of Diderrich-Kneser's and Hamidoune's theorems on
sumsets and Tao's theorem on sets of small doubling. In passing we classify the
finite-dimensional algebras over infinite fields with finitely many
subalgebras. These algebras play a crucial role in our linear version of
Diderrich-Kneser's theorem. We also explain how the original theorems for
groups we linearize can be easily deduced from our results applied to group
algebras. Finally, we give lower bounds for the Minkowski product of two
subsets in finite monoids by using their associated monoid algebras.Comment: In this second version, we clarify and extend the domain of validity
of Diderrich-Kneser's theorem for associative algebras. We simplify the
proofs and we also add a section on Kneser's and Hamidoune's theorem in
monoi
Algebraic rational cells and equivariant intersection theory
We provide a notion of algebraic rational cell with applications to
intersection theory on singular varieties with torus action. Based on this
notion, we study the algebraic analogue of -filtrable varieties:
algebraic varieties where a torus acts with isolated fixed points, such that
the associated Bialynicki-Birula decomposition consists of algebraic rational
cells. We show that the rational equivariant Chow group of any
-filtrable variety is freely generated by the cell closures. We
apply this result to group embeddings, and more generally to spherical
varieties. This paper is an extension of arxiv.org/abs/1112.0365 to equivariant
Chow groups.Comment: Second version. 24 pages. Substantial changes in the presentation. In
particular, the results on Poincar\'e duality (Section 6 of first version)
are omitted; they are published in a separate paper (see
http://revistas.pucp.edu.pe/index.php/promathematica/article/view/11235
On v-Marot Mori rings and C-rings
C-domains are defined via class semigroups, and every C-domain is a Mori
domain with nonzero conductor whose complete integral closure is a Krull domain
with finite class group. In order to extend the concept of C-domains to rings
with zero divisors, we introduce -Marot rings as generalizations of ordinary
Marot rings and study their theory of regular divisorial ideals. Based on this
we establish a generalization of a result well-known for integral domains. Let
be a -Marot Mori ring, its complete integral closure, and
suppose that the conductor is regular. If the
residue class ring and the class group
are both finite, then is a C-ring. Moreover, we study both -Marot rings
and C-rings under various ring extensions.Comment: Journal of the Korean Mathematical Society, to appea
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