38,566 research outputs found
On the dimension of polynomial semirings
In our previous work, motivated by the study of tropical polynomials, a
definition for prime congruences was given for an arbitrary commutative
semiring. It was shown that for additively idempotent semirings this class
exhibits some analogous properties to prime ideals in ring theory. The current
paper focuses on the resulting notion of Krull dimension, which is defined as
the length of the longest chain of prime congruences. Our main result states
that for any additively idempotent semiring , the semiring of polynomials
and the semiring of Laurent polynomials , we have
Diffeological Clifford algebras and pseudo-bundles of Clifford modules
We consider the diffeological version of the Clifford algebra of a
(diffeological) finite-dimensional vector space; we start by commenting on the
notion of a diffeological algebra (which is the expected analogue of the usual
one) and that of a diffeological module (also an expected counterpart of the
usual notion). After considering the natural diffeology of the Clifford
algebra, and its expected properties, we turn to our main interest, which is
constructing pseudo-bundles of diffeological Clifford algebras and those of
diffeological Clifford modules, by means of the procedure called diffeological
gluing. The paper has a significant expository portion, regarding mostly
diffeological algebras and diffeological vector pseudo-bundles.Comment: 35 pages; exposition improved, an example adde
Proper twin-triangular Ga-actions on A^4 are translations
An additive group action on an affine 3 -space over a complex Dedekind domain
A is said to be twin-triangular if it is generated by a locally nilpotent
derivation of A[y,z,t] of the form rd/dy+p(y)d/dz + q(y)d/dt, where r belongs
to A and p,q belong to A[y] . We show that these actions are translations if
and only if they are proper. Our approach avoids the computation of rings of
invariants and focuses more on the nature of geometric quotients for such
actions
Contractions of Lie algebras and algebraic groups
Degenerations, contractions and deformations of various algebraic structures
play an important role in mathematics and physics. There are many different
definitions and special cases of these notions. We try to give a general
definition which unifies these notions and shows the connections among them.
Here we focus on contractions of Lie algebras and algebraic groups
Cluster-tilted algebras without clusters
Cluster-tilted algebras are trivial extensions of tilted algebras. This
correspondence induces a surjective map from tilted algebras to cluster-tilted
algebras. If B is a cluster-tilted algebra, we use the fibre of B under this
map to study the module category of B. In particular, we introduce the notion
of reflections of tilted algebras and define an algorithm that constructs the
transjective component of the Auslander-Reiten quiver of cluster-tilted
algebras of tree type.Comment: 37 page
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