81 research outputs found
Duality of Anderson -motives having
This paper extends the main result of the paper "Duality of Anderson
-motives", that the lattice of the dual of a t-motive is the dual
lattice of , to the case when the nilpotent operator of is non-zero.Comment: 21 pages; minor correction
Lattice map for Anderson t-motives : first approach
There exists a lattice map from the set of pure uniformizable Anderson
t-motives to the set of lattices. It is not known what is the image and the
fibers of this map. We prove a local result that sheds the first light to this
problem and suggests that maybe this map is close to 1 -- 1. Namely, let
be a t-motive of dimension and rank \ --- \ the -th power of the
Carlitz module of rank 2, and let be a t-motive which is in some sense
"close" to . We consider the lattice map , where
is a lattice in . We show that the lattice map is an isomorphism in a
"neighborhood" of . Namely, we compare the action of monodromy groups:
(a) from the set of equations defining t-motives to the set of t-motives
themselves, and (b) from the set of Siegel matrices to the set of lattices. The
result of the present paper gives that the size of a neighborhood, where we
have an isomorphism, depends on an element of the monodromy group. We do not
know whether there exists a universal neighborhood. Method of the proof:
explicit solution of an equation describing an isomorphism between two
t-motives by a method of successive approximations using a version of the
Hensel lemma.Comment: 26 pages. Minor improvement
Kimmerle conjecture for the Held and O'Nan sporadic simple groups
Using the Luthar--Passi method, we investigate the Zassenhaus and Kimmerle
conjectures for normalized unit groups of integral group rings of the Held and
O'Nan sporadic simple groups. We confirm the Kimmerle conjecture for the Held
simple group and also derive for both groups some extra information relevant to
the classical Zassenhaus conjecture.Comment: 9 page
On a construction of self-dual gauge fields in seven dimensions
We consider gauge fields associated with a semisimple Malcev algebra. We
construct a gauge-invariant Lagrangian and found a solution of modified
Yang-Mills equations in seven dimensions.Comment: 10 pages, LaTeX, no figure
Kimmerle conjecture for the Held and O'Nan sporadic simple groups
Using the Luthar--Passi method, we investigate the Zassenhaus and
Kimmerle conjectures for normalized unit groups of integral group rings of the
Held and O'Nan sporadic simple groups. We confirm the Kimmerle conjecture for
the Held simple group and also derive for both groups some extra information
relevant to the classical Zassenhaus conjecture
On filtered multiplicative bases of some associative algebras
We deal with the existing problem of filtered multiplicative bases of
finite-dimensional associative algebras. For an associative algebra A over a
field, we investigate when the property of having a filtered multiplicative
basis is hereditated by homomorphic images or by the associated graded algebra
of . These results are then applied to some classes of group algebras and
restricted enveloping algebras.Comment: 10 page
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