Search results for "General Mathematics"
showing 10 items of 3795 documents
LEFT INVARIANT COMPLEX STRUCTURES ON NILPOTENT SIMPLY CONNECTED INDECOMPOSABLE 6-DIMENSIONAL REAL LIE GROUPS
2007
Integrable complex structures on indecomposable 6-dimensional nilpotent real Lie algebras have been computed in a previous paper, along with normal forms for representatives of the various equivalence classes under the action of the automorphism group. Here we go to the connected simply connected Lie group G0 associated to such a Lie algebra đ¤. For each normal form J of integrable complex structures on đ¤, we consider the left invariant complex manifold G = (G0, J) associated to G0 and J. We explicitly compute a global holomorphic chart for G and we write down the multiplication in that chart.
Star-polynomial identities: computing the exponential growth of the codimensions
2017
Abstract Can one compute the exponential rate of growth of the â-codimensions of a PI-algebra with involution â over a field of characteristic zero? It was shown in [2] that any such algebra A has the same â-identities as the Grassmann envelope of a finite dimensional superalgebra with superinvolution B. Here, by exploiting this result we are able to provide an exact estimate of the exponential rate of growth e x p â ( A ) of any PI-algebra A with involution. It turns out that e x p â ( A ) is an integer and, in case the base field is algebraically closed, it coincides with the dimension of an admissible subalgebra of maximal dimension of B.
On Shimura subvarieties generated by families of abelian covers ofP1
2018
We investigate the occurrence of Shimura (special) subvarieties in the locus of Jacobians of abelian Galois covers of P1 in Ag and give classifications of families of such covers that give rise to Shimura subvarieties in the Torelli locus Tg inside Ag. Our methods are based on MoonenâOort works as well as characteristic p techniques of Dwork and Ogus and Monodromy computations.
Group algebras and Lie nilpotence
2013
Abstract Let â be an involution of a group algebra FG induced by an involution of the group G. For char F â 2 , we classify the groups G with no 2-elements and with no nonabelian dihedral groups involved whose Lie algebra of â-skew elements is nilpotent.
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 â and let c n â ( A ) be its sequence of â-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 â-algebras: the group algebra of Z 2 and a 4-dimensional subalgebra of the 4 Ă 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 â-algebras, up to T 2 â -equivalence, generating varieties of almost polynomial grâŚ
Fixed point theorems for non-self mappings in symmetric spaces under Ď-weak contractive conditions and an application to functional equations in dynaâŚ
2014
In this paper, we prove some common fixed point theorems for two pairs of non-self weakly compatible mappings enjoying common limit range property, besides satisfying a generalized phi-weak contractive condition in symmetric spaces. We furnish some illustrative examples to highlight the realized improvements in our results over the corresponding relevant results of the existing literature. We extend our main result to four finite families of mappings in symmetric spaces using the notion of pairwise commuting mappings. Finally, we utilize our results to discuss the existence and uniqueness of solutions of certain system of functional equations arising in dynamic programming.
Codimension growth and minimal superalgebras
2003
A celebrated theorem of Kemer (1978) states that any algebra satisfying a polynomial identity over a field of characteristic zero is PI-equivalent to the Grassmann envelope G(A) of a finite dimensional superalgebra A. In this paper, by exploiting the basic properties of the exponent of a PI-algebra proved by Giambruno and Zaicev (1999), we define and classify the minimal superalgebras of a given exponent over a field of characteristic zero. In particular we prove that these algebras can be realized as block-triangular matrix algebras over the base field. The importance of such algebras is readily proved: A is a minimal superalgebra if and only if the ideal of identities of G(A) is a productâŚ
Serial subalgebras of finitary Lie algebras
2000
A Lie subalgebra L of glK(V ) is said to be finitary if it consists of elements of finite rank. We show that, if L acts irreducibly on V , and if V is infinite-dimensional, then every non-trivial ascendant Lie subalgebra of L acts irreducibly on V too. When CharK 6= 2, it follows that the locally solvable radical of such L is trivial. In general, locally solvable finitary Lie algebras over fields of characteristic 6= 2 are hyperabelian.
Gleason Parts and Weakly Compact Homomorphismsbetween Uniform Banach Algebras
1999
If points in nontrivial Gleason parts of a uniform Banach algebra have unique representing measures, then the weak and the norm topology coincide on the spectrum. We derive from this several consequences about weakly compact homomorphisms and discuss the case of other uniform Banach algebras arising in complex infinite dimensional analysis.