263 research outputs found
Classification of finite congruence-simple semirings with zero
Our main result states that a finite semiring of order >2 with zero which is
not a ring is congruence-simple if and only if it is isomorphic to a `dense'
subsemiring of the endomorphism semiring of a finite idempotent commutative
monoid.
We also investigate those subsemirings further, addressing e.g. the question
of isomorphy.Comment: 16 page
Sobre el ph. d. en matemáticas
Casi todos los aspectos de la educación universitaria en los Estados Unidos están siendo examinados y revaluados en la época presente. Se siente una necesidad de echar una nueva ojeada a la naturaleza del grado de Ph.D. en Matemáticas asà como a las premisas que lo han llevado a su forma presente
Topics in Cubic Special Geometry
We reconsider the sub-leading quantum perturbative corrections to N=2 cubic
special Kaehler geometries. Imposing the invariance under axion-shifts, all
such corrections (but the imaginary constant one) can be introduced or removed
through suitable, lower unitriangular symplectic transformations, dubbed
Peccei-Quinn (PQ) transformations. Since PQ transformations do not belong to
the d=4 U-duality group G4, in symmetric cases they generally have a
non-trivial action on the unique quartic invariant polynomial I4 of the charge
representation R of G4. This leads to interesting phenomena in relation to
theory of extremal black hole attractors; namely, the possibility to make
transitions between different charge orbits of R, with corresponding change of
the supersymmetry properties of the supported attractor solutions. Furthermore,
a suitable action of PQ transformations can also set I4 to zero, or vice versa
it can generate a non-vanishing I4: this corresponds to transitions between
"large" and "small" charge orbits, which we classify in some detail within the
"special coordinates" symplectic frame. Finally, after a brief account of the
action of PQ transformations on the recently established correspondence between
Cayley's hyperdeterminant and elliptic curves, we derive an equivalent,
alternative expression of I4, with relevant application to black hole entropy.Comment: 1+39 page
On swapping the states of two qudits
The SWAP gate has become an integral feature of quantum circuit architectures
and is designed to permute the states of two qubits through the use of the
well-known controlled-NOT gate. We consider the question of whether a two-qudit
quantum circuit composed entirely from instances of the generalised
controlled-NOT gate can be constructed to permute the states of two qudits.
Arguing via the signature of a permutation, we demonstrate the impossibility of
such circuits for dimensions (mod 4)
Commutator Leavitt path algebras
For any field K and directed graph E, we completely describe the elements of
the Leavitt path algebra L_K(E) which lie in the commutator subspace
[L_K(E),L_K(E)]. We then use this result to classify all Leavitt path algebras
L_K(E) that satisfy L_K(E)=[L_K(E),L_K(E)]. We also show that these Leavitt
path algebras have the additional (unusual) property that all their Lie ideals
are (ring-theoretic) ideals, and construct examples of such rings with various
ideal structures.Comment: 24 page
A Lie algebra variation on a theorem of Wedderburn
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28978/1/0000005.pd
Number-Theoretic Nature of Communication in Quantum Spin Systems
The last decade has witnessed substantial interest in protocols for
transferring information on networks of quantum mechanical objects. A variety
of control methods and network topologies have been proposed, on the basis that
transfer with perfect fidelity --- i.e. deterministic and without information
loss --- is impossible through unmodulated spin chains with more than a few
particles. Solving the original problem formulated by Bose [Phys. Rev. Lett.
91, 207901 (2003)], we determine the exact number of qubits in unmodulated
chains (with XY Hamiltonian) that permit the transfer with fidelity arbitrarily
close to 1, a phenomenon called pretty good state transfer. We prove that this
happens if and only if the number of nodes is n=p-1, 2p-1, where p is a prime,
or n=2^{m}-1. The result highlights the potential of quantum spin system
dynamics for reinterpreting questions about the arithmetic structure of
integers, and, in this case, primality.Comment: 6 pages, 1 EPS figur
On subgroups in division rings of type
Let be a division ring with center . We say that is a {\em
division ring of type } if for every two elements the division
subring is a finite dimensional vector space over . In this paper
we investigate multiplicative subgroups in such a ring.Comment: 10 pages, 0 figure
On minimal extensions of rings
Given two rings , is said to be a minimal ring extension
of if is a maximal subring of . In this article, we study minimal
extensions of an arbitrary ring , with particular focus on those possessing
nonzero ideals that intersect trivially. We will also classify the minimal
ring extensions of prime rings, generalizing results of Dobbs, Dobbs & Shapiro,
and Ferrand & Olivier on commutative minimal extensions.Comment: 25 page
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