Volume 26, Issue 2

Let M be a reductive monoid. If e is an idempotent in M , we prove that the centralizer M ( e ) of e in M is a regular monoid with a finite graded poset of 𝒥-classes. We compute this poset explicitly when M is of canonical or dual canonical type and e is the relevant pivotal idempotent.

We prove that, except for a few explicit roots of unity, the quantum image of any Johnson subgroup of the mapping class group contains an explicit free non-abelian subgroup.

Based on an idea of Y. Péresse and some results of Maltcev, Mitchell and Ruškuc, we present sufficient conditions under which the endomorphism monoid of a countably infinite ultrahomogeneous first-order structure has the Bergman property. This property has played a prominent role both in the theory of infinite permutation groups and, more recently, in semigroup theory. As a byproduct of our considerations, we establish a criterion for a countably infinite ultrahomogeneous structure to be homomorphism-homogeneous.

The Dirichlet and Neumann problems of heat equation with certain potentials of the form ∂t-Δ+V=0$\partial _t-\Delta +V=0$ in Lipschitz cylinders are studied, where V is a nonnegative potential satisfying certain conditions.

This paper gives the additivity and reduction formulas for mixed multiplicities of multi-graded modules M and mixed multiplicities of arbitrary ideals, and establishes the recursion formulas for the sum of all the mixed multiplicities of M . As an application of these formulas we get the recursion formulas for the multiplicity of multi-graded Rees modules.

Let K be a skew field and (G,<)$(G,&lt;)$ be an ordered group. We show that the skew field generated by the group ring K[G]$K[G]$ inside the Malcev–Neumann series ring K((G;<))$K((G;&lt;))$ contains noncommutative free group algebras.

Decomposition theorems for Q K spaces of analytic functions are established. As an application, we give a characterization of interpolation by functions in Q K spaces.

We show how to compute a Macaulay dual class in local cohomology H𝔪n(𝔽[V])$\hspace*{-0.56905pt}H^n_\mathfrak {m}(\mathbb {F}[V])\hspace*{-0.85358pt}$ for an given ideal I(𝒮)⊂𝔽[V]$I(\mathcal {S}) \subset \mathbb {F}[V]$ of generalized invariants associated to a set of reflections 𝒮⊂GL(n,𝔽)$\mathcal {S} \subset \text{GL}(n, \mathbb {F})$ that generate a finite subgroup G(𝒮)≤GL(n,𝔽)$G(\mathcal {S}) \le \text{GL}(n, \mathbb {F})$. We then apply this in the case that the coinvariant algebra 𝔽[V]G(𝒮)$\mathbb {F}[V]_{G(\mathcal {S})}$ is a fixed point free Poincaré duality algebra to obtain a Macaulay dual for the Hilbert ideal 𝔥(G(𝒮))$\mathfrak {h}(G(\mathcal {S}))$ of G(𝒮)$G(\mathcal {S})$.

We consider the logarithm of the central value logL(1/2)$\log L(1/2)$ in the orthogonal family {L(s,f)}f∈Hk$\lbrace L(s,f)\rbrace _{f \in H_k}$ where H k is the set of weight k Hecke-eigen cusp forms for SL2(ℤ)$\text{SL}_2(\mathbb {Z})$, and in the symplectic family {L(s,χ8d)}d≍D$\lbrace L(s,\chi _{8d})\rbrace _{d \asymp D}$ where χ8d$\chi _{8d}$ is the real character associated to fundamental discriminant 8d$8d$. Unconditionally, we prove that the two distributions are asymptotically bounded above by Gaussian distributions, in the first case of mean -1/2loglogk$-1/2 \log \log k$ and variance loglogk$\log \log k$, and in the second case of mean 1/2loglogD$1/2\log \log D$ and variance loglogD$\log \log D$. Assuming both the Riemann and Zero Density Hypotheses in these families we obtain the full normal law in both families, confirming a conjecture of Keating and Snaith.

We answer in the affirmative a question posed by Ivanov and Vassilev on the existence of a seven-dimensional quaternionic contact manifold with closed fundamental 4-form and non-vanishing torsion endomorphism. Moreover, we show an approach to the classification of seven-dimensional solvable Lie groups having an integrable left invariant quaternionic contact structure. In particular, we prove that the unique seven-dimensional nilpotent Lie group admitting such a structure is the quaternionic Heisenberg group.

We consider a Weitzenböck derivation Δ acting on a polynomial ring R=K[ξ1,ξ2,...,ξm]$ R=K[\xi _1,\xi _2,\ldots ,\xi _m] $ over a field K of characteristic 0. The K -algebra RΔ={h∈R∣Δ(h)=0}${R^\Delta = \lbrace h \in R \mid \Delta (h) = 0\rbrace }$ is called the algebra of constants. Nowicki considered the case where the Jordan matrix for Δ acting on R 1 , the degree 1 component of R , has only Jordan blocks of size 2. He conjectured that a certain set generates RΔ$R^{\Delta }$ in that case. Recently Khoury, Drensky and Makar-Limanov and Kuroda have given proofs of Nowicki's conjecture. Here we consider the case where the Jordan matrix for Δ acting on R 1 has only Jordan blocks of size at most 3. We use combinatorial methods to give a minimal set of generators 𝒢 for the algebra of constants RΔ$R^{\Delta }$. Moreover, we show how our proof yields an algorithm to express any h∈RΔ$h \in R^\Delta $ as a polynomial in the elements of 𝒢. In particular, our solution shows how the classical techniques of polarization and restitution may be used to augment the techniques of SAGBI bases to construct generating sets for subalgebras.

We construct a topological cellular operad such that the algebras over its cellular chains are the homotopy unital A -infinity algebras of Fukaya–Oh–Ohta–Ono.

This paper aims to prove that the norm of the L p -Fourier transform of the semidirect product ℝn⋊K$\mathbb {R}^n\rtimes K$ is A p n , where 1<p≤2$1 &lt; p \le 2$, q=p/(p-1)$q=p/(p-1)$, Ap=p12pq-12q$A_p=p^{\frac{1}{2p}}q^{\frac{-1}{2q}}$, and K stands for a compact subgroup of automorphisms of ℝ n . An extremal function is given by an extension of a Gaussian function. Besides, as an example of non-compact extension, the universal covering group of the Euclidean motion group of the plane is also treated and an estimate of the norm is obtained.

The aim of this paper is to show that there is no semifield of order q 8 , q an odd prime, over 𝔽 q , which admits an elementary abelian 2-group E ≅ 2 3 of automorphisms.