Under study are the right-symmetric algebras over a field
which possess a “unital” matrix subalgebra
. We classify all these finite-dimensional right-symmetric algebras
in the case when
is an ...irreducible module over
.
TOPAS and its academic variant TOPAS‐Academic are nonlinear least‐squares optimization programs written in the C++ programming language. This paper describes their functionality and architecture. The ...latter is of benefit to developers seeking to reduce development time. TOPAS allows linear and nonlinear constraints through the use of computer algebra, with parameter dependencies, required for parameter derivatives, automatically determined. In addition, the objective function can include restraints and penalties, which again are defined using computer algebra. Of importance is a conjugate gradient solution routine with bounding constraints which guide refinements to convergence. Much of the functionality of TOPAS is achieved through the use of generic functionality; for example, flexible peak‐shape generation allows neutron time‐of‐flight (TOF) peak shapes to be described using generic functions. The kernel of TOPAS can be run from the command line for batch mode operation or from a closely integrated graphical user interface. The functionality of TOPAS includes peak fitting, Pawley and Le Bail refinement, Rietveld refinement, single‐crystal refinement, pair distribution function refinement, magnetic structures, constant wavelength neutron refinement, TOF refinement, stacking‐fault analysis, Laue refinement, indexing, charge flipping, and structure solution through simulated annealing.
TOPAS is nonlinear least‐squares optimization computer program written primarily for the analysis of crystallographic problems.
We give a complete description of degenerations of complex 5-dimensional nilpotent associative commutative algebras. As corollary, we have the description of all rigid algebras in the variety of ...5-dimensional commutative Leibniz algebras.
The aim of this thesis is to study both holomorphic and algebraic flows on Shimura varieties. The first part of the thesis studies holomorphic flows, the main result is a hyperbolic analogue of the ...Bloch-Ochiai Theorem in the context of mixed Shimura varieties. This extends previous results of Ullmo and Yafaev for co-compact pure Shimura varieties. The proof follows the template set by the hyperbolic Ax-Linedmann-Weierstrass theorem of using the PilaWilkie counting theorem together with some volume inequalities to prove our result. The heart of the proof consists of two volume inequalities, first one for the intersection of a definable set with hyperbolic balls in Hermitian symmetric domains of non-compact type. The second for the intersection of a definable portion of a holomorphic curve with a fundamental domain for the action of a congruence group on a Hermitian symmetric domain of non-compact type. In the second part we study totally geodesic subvarieties of mixed Shimura varieties and algebraic flows. We show that contrary to the case of pure Shimura varieties, there is in general no inclusion either way between the concept of weakly special and totally geodesic subvariety in the mixed setting. Then we report an argument communicated by N. Mok which shows that unlike in the pure case there are totally geodesic submanifolds of a mixed Shimura variety that are not homogeneous. Finally we use these results on totally geodesic subvarieties to state and prove a generalisation of results of Ullmo and Yafaev on algebraic flows on pure Shimura varieties to the mixed case. The proof follows the pure case and uses a theorem of Ratner in arithmetic dynamics.
On n-cubic Pyramid Algebras Guo, Jin Yun; Luo, Deren
Algebras and representation theory,
08/2016, Volume:
19, Issue:
4
Journal Article
Peer reviewed
Open access
In this paper we study a class of algebras having
n
-dimensional pyramid shaped quiver with
n
-cubic cells, which we called
n
-cubic pyramid algebras. This class of algebras includes the quadratic ...dual of the basic
n
-Auslander absolutely
n
-complete algebras introduced by Iyama. We show that the projective resolutions of the simples of
n
-cubic pyramid algebras can be characterized by
n
-cuboids, and prove that they are periodic. So these algebras are almost Koszul and (
n
−1)-translation algebras. We also recover Iyama’s cone construction for
n
-Auslander absolutely
n
-complete algebras using
n
-cubic pyramid algebras and the theory of
n
-translation algebras.
We prove analogs of A. Selberg’s result for finitely generated subgroups of
Aut
(
A
)
\operatorname {Aut}(A)
and of Engel’s theorem for subalgebras of
Der
(
A
)
\operatorname {Der}(A)
for a ...finitely generated associative commutative algebra
A
A
over an associative commutative ring. We prove also an analog of the theorem of W. Burnside and I. Schur about local finiteness of torsion subgroups of
Aut
(
A
)
\operatorname {Aut}(A)
.
We study algebraic conditions when a pseudo MV-algebra is an interval in the lexicographic product of an Abelian unital linearly ordered group and an ℓ-group that is not necessarily Abelian. We ...introduce two classes of pseudo MV-algebras which can be split into a system of comparable slices indexed by elements of an interval in an Abelian linearly ordered group. We show when such pseudo MV-algebras have a representation by a lexicographic product with an ℓ-group. Fixing a unital ℓ-group, we show that the category of such pseudo MV-algebras is categorically equivalent to the category of ℓ-groups.
We introduce an algebraic version of the Katsura
C
∗
-algebra of a pair
A
,
B
of integer matrices and an algebraic version of the Exel–Pardo
C
∗
-algebra of a self-similar action on a graph. We prove ...a Graded Uniqueness Theorem for such algebras and construct a homomorphism of the latter into a Steinberg algebra that, under mild conditions, is an isomorphism. Working with Steinberg algebras over non-Hausdorff groupoids we prove that in the unital case, our algebraic version of Katsura
C
∗
-algebras are all isomorphic to Steinberg algebras.
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