Search results for "BVAR"
showing 10 items of 16 documents
The generic local structure of time-optimal synthesis with a target of codimension one in dimension greater than two
1997
In previous papers, we gave in dimension 2 and 3 a classification of generic synthesis of analytic systems\(\dot v(t) = X(v(t)) + u(t)Y(v(t))\) with a terminal submanifoldN of codimension one when the trajectories are not tangent toN. We complete here this classification in all generic cases in dimension 3, giving a topological classification and a model in each case. We prove also that in dimensionn≥3, out of a subvariety ofN of codimension there, we have described all the local synthesis.
The effects of monetary policy on income and wealth inequality in the U.S. Exploring different channels
2020
We assess the effects of monetary policy shocks on income and wealth inequality through direct inequality measures and by analyzing several transmission channels explored in recent literature. Furthermore, we analyze two additional channels: the Housing and the Fiscal channels. The methodology adopted is a Bayesian proxy SVAR using a high-frequency identification based on the external instruments approach. Our own policy shocks are constructed for this purpose. The results show that an expansionary monetary policy shock does not have a significant effect on income inequality due to the existence of opposite channels, whereas it increases wealth inequality mainly through the portfolio channe…
Polynomial codimension growth of algebras with involutions and superinvolutions
2017
Abstract Let A be an associative algebra over a field F of characteristic zero endowed with a graded involution or a superinvolution ⁎ and let c n ⁎ ( A ) be its sequence of ⁎-codimensions. In [4] , [12] it was proved that if A is finite dimensional such sequence is polynomially bounded if and only if A generates a variety not containing a finite number of ⁎-algebras: the group algebra of Z 2 and a 4-dimensional subalgebra of the 4 × 4 upper triangular matrices with suitable graded involutions or superinvolutions. In this paper we focus our attention on such algebras since they are the only finite dimensional ⁎-algebras, up to T 2 ⁎ -equivalence, generating varieties of almost polynomial gr…
Polynomial growth and star-varieties
2016
Abstract Let V be a variety of associative algebras with involution over a field F of characteristic zero and let c n ⁎ ( V ) , n = 1 , 2 , … , be its ⁎-codimension sequence. Such a sequence is polynomially bounded if and only if V does not contain the commutative algebra F ⊕ F , endowed with the exchange involution, and M, a suitable 4-dimensional subalgebra of the algebra of 4 × 4 upper triangular matrices. Such algebras generate the only varieties of ⁎-algebras of almost polynomial growth, i.e., varieties of exponential growth such that any proper subvariety is polynomially bounded. In this paper we completely classify all subvarieties of the ⁎-varieties of almost polynomial growth by gi…
Subvarieties of the Varieties Generated by the SuperalgebraM1, 1(E) orM2(𝒦)
2003
Abstract Let 𝒦 be a field of characteristic zero, and let us consider the matrix algebra M 2(𝒦) endowed with the ℤ2-grading (𝒦e 11 ⊕ 𝒦e 22) ⊕ (𝒦e 12 ⊕ 𝒦e 21). We define two superalgebras, ℛ p and 𝒮 q , where p and q are positive integers. We show that if 𝒰 is a proper subvariety of the variety generated by the superalgebra M 2(𝒦), then the even-proper part of the T 2-ideal of graded polynomial identities of 𝒰 asymptotically coincides with the even-proper part of the graded polynomial identities of the variety generated by the superalgebra ℛ p ⊕ 𝒮 q . This description also affords an even-asymptotic desc…
Stabilization of the cohomology of thickenings
2016
For a local complete intersection subvariety $X=V({\mathcal I})$ in ${\mathbb P}^n$ over a field of characteristic zero, we show that, in cohomological degrees smaller than the codimension of the singular locus of $X$, the cohomology of vector bundles on the formal completion of ${\mathbb P}^n$ along $X$ can be effectively computed as the cohomology on any sufficiently high thickening $X_t=V({\mathcal I^t})$; the main ingredient here is a positivity result for the normal bundle of $X$. Furthermore, we show that the Kodaira vanishing theorem holds for all thickenings $X_t$ in the same range of cohomological degrees; this extends the known version of Kodaira vanishing on $X$, and the main new…
Varieties of almost polynomial growth: classifying their subvarieties
2007
Let G be the infinite dimensional Grassmann algebra over a field F of characteristic zero and UT2 the algebra of 2 x 2 upper triangular matrices over F. The relevance of these algebras in PI-theory relies on the fact that they generate the only two varieties of almost polynomial growth, i.e., they grow exponentially but any proper subvariety grows polynomially. In this paper we completely classify, up to PI-equivalence, the associative algebras A such that A is an element of Var(G) or A is an element of Var(UT2).
Superalgebras with Involution or Superinvolution and Almost Polynomial Growth of the Codimensions
2018
Let A be a superalgebra with graded involution or superinvolution ∗ and let $c_{n}^{*}(A)$, n = 1,2,…, be its sequence of ∗-codimensions. In case A is finite dimensional, in Giambruno et al. (Algebr. Represent. Theory 19(3), 599–611 2016, Linear Multilinear Algebra 64(3), 484–501 2016) it was proved that such a sequence is polynomially bounded if and only if the variety generated by A does not contain the group algebra of $\mathbb {Z}_{2}$ and a 4-dimensional subalgebra of the 4 × 4 upper-triangular matrices with suitable graded involutions or superinvolutions. In this paper we study the general case of ∗-superalgebras satisfying a polynomial identity. As a consequence we classify the varie…
On the Oort conjecture for Shimura varieties of unitary and orthogonal types
2014
In this paper we study the Oort conjecture on Shimura subvarieties contained generically in the Torelli locus in the Siegel modular variety $\mathcal{A}_g$. Using the poly-stability of Higgs bundles on curves and the slope inequality of Xiao on fibred surfaces, we show that a Shimura curve $C$ is not contained generically in the Torelli locus if its canonical Higgs bundles contains a unitary Higgs subbundle of rank at least $(4g+2)/5$. From this we prove that a Shimura subvariety of $\mathbf{SU}(n,1)$-type is not contained generically in the Torelli locus when a numerical inequality holds, which involves the genus $g$, the dimension $n+1$, the degree $2d$ of CM field of the Hermitian space,…
Varieties of algebras with pseudoinvolution and polynomial growth
2017
Let A be an associative algebra with pseudoinvolution (Formula presented.) over an algebraically closed field of characteristic zero and let (Formula presented.) be its sequence of (Formula presented.) -codimensions. We shall prove that such a sequence is polynomially bounded if and only if the variety generated by A does not contain five explicitly described algebras with pseudoinvolution. As a consequence, we shall classify the varieties of algebras with pseudoinvolution of almost polynomial growth, i.e. varieties of exponential growth such that any proper subvariety has polynomial growth and, along the way, we shall give also the classification of their subvarieties. Finally, we shall de…