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A Note on Invariantly Finitely $L$-Presented Groups
Tietze transformations infinite presentations recursive presentations selfsimilar groups
2012/5/9
In the first part of this note, we introduce Tietze transformations for $L$-presentations. These transformations enable us to generalize Tietze's theorem for finitely presented groups to invariantly f...
A note on the Triple Product Property subgroup capacity of finite groups
Triple Product Property finite groups Group Theory
2011/9/23
Abstract: In the context of group-theoretic fast matrix multiplication the TPP capacity is used to bound the exponent $\omega$ of matrix multiplication. We prove a new and sharper upper bound for the ...
A note on the computation of the Frobenius number of a numerical semigroup
numerical semigroup Frobenius number monomial curve semigroup ideal
2011/8/26
Abstract: In this article we present a formula for the computation of the Frobenius number and the conductor of a numerical semigroup from the sockel of a quotient of certain semigroup ring.
Abstract: A ring $R$ is called right SSP (SIP) if the sum (intersection) of any two direct summands of $R_{R}$ is also a direct summand. Left sides can be defined similarly. The following are equivale...
Note on a relation between Randic index and algebraic connectivity
Randi´ c index algebraic connectivity edge connectivity diameter
2011/2/24
A conjecture of AutoGraphiX on the relation between the Randi´c index R and the algebraic connectivity a of a connected graph G is:R a n − 3 + 2p2 2 ! / 2(1 − cos n ) with ...
A note on the $O_q(\hat{sl_2})$ algebra
Current algebra q− Onsager algebra Quantum integrable models
2011/2/25
An explicit homomorphism that relates the elements of the infinite dimensional non-Abelian
algebra generating Oq(csl2) currents and the standard generators of the q−Onsager algebra is proposed....
A note on the Frobenius morphism on toric varieties
note Frobenius morphism toric varieties
2011/1/20
We give a new, shorter computation of Frobenius push-forwards of line bundles on toric varieties.
Let A be an affine algebra of dimension d>3 over the field k, where k is the algebraic closure of the finite field Z/pZ, where p\geq d. Let P be a projective A-module of rank d-1. Then P is cancellati...
A Note on Singular Moduli Spaces of Sheaves on K3 Surfaces
Singular Moduli Spaces K3 Surfaces
2010/11/24
This paper studies deformations and birational maps between singular moduli spaces of semistable sheaves with 2-divisible Mukai vectors on K3 surfaces. It is showed that under certain conditions, two...
A Note on Formality and Singularities of Moduli Spaces
Formality Singularities Moduli Spaces
2010/11/24
This paper studies formality of the differential graded algebra $RHom(E,E)$, where $E$ is a semistable sheaf on a K3 surface. The main tool is Kaledin's theorem on formality in families. For a large ...
A note on Gaussian correlation inequalities for nonsymmetric sets
Gaussian correlation inequalities nonsymmetric sets
2010/11/23
We consider the Gaussian correlation inequality for nonsymmetric convex sets. More precisely, if $A\subset\mathbb{R}^d$ is convex and the origin $0\in A$, then for any ball $B$ centered at the origin...
A note on V-binomials recurrence for Lucas companion to $U_n$ sequence $V_n$
V-binomials recurrence Lucas companion
2010/11/19
The looked for V-binomials recurrence for Lucas companion to $U_n$ sequence $V_n$ is delivered
In this note, we will prove that a finite dimensional Lie algebra $L$ of characteristic zero, admitting an abelian algebra of derivations $D\leq Der(L)$ with the property $$ L^n\subseteq \sum_{d\in D...
A note on trace scaling actions and fundamental groups of $C^*$-algebras
Fundamental group Trace scaling action Dimension group
2010/12/1
Using Effros-Handelman-Shen theorem and Elliott’s classification theorem of AF algebras, we show that there exists a unital simple AF algebra A with unique trace such that A K admits no trace scaling ...
A note on $(\alpha, \beta)$-higher derivations and their extensions to modules of quotients
derivation higher derivation ring of quotients module of quotients
2010/12/3
We extend some recent results on the differentiability of torsion theories. In particular, we generalize the concept of ( , )-derivation to ( , )-higher derivation and demonstrate that a filter of a...