Let g = W1 be the Witt algebra over an algebraically closed field k of characteristic p 〉 3, and let ∮（g） = {（x,y） ∈ g×g [x,y] = 0} be the commuting variety of g. In contrast with the case of classical Lie...Let g = W1 be the Witt algebra over an algebraically closed field k of characteristic p 〉 3, and let ∮（g） = {（x,y） ∈ g×g [x,y] = 0} be the commuting variety of g. In contrast with the case of classical Lie algebras of P. Levy [J. Algebra, 2002, 250： 473-484], we show that the variety ∮（g） is reducible, and not equidimensional. Irreducible components of ∮（g） and their dimensions are precisely given. As a consequence, the variety ∮（g） is not normal.展开更多
In this paper, all subvarieties of the varieties Ak （k ∈N） generated by aperiodic commutative semigroups are characterized. Based on this characterization, the structure of lattice of subvarieties of Ak is investig...In this paper, all subvarieties of the varieties Ak （k ∈N） generated by aperiodic commutative semigroups are characterized. Based on this characterization, the structure of lattice of subvarieties of Ak is investigated.展开更多
Many of people have tried to obtain the structure of Baer-invariant of groups exactly. Recently, B. Mashayekhy and M. Parvizi determine Baer-invariant of finitely generated Abelian groups. Also, it is done for some no...Many of people have tried to obtain the structure of Baer-invariant of groups exactly. Recently, B. Mashayekhy and M. Parvizi determine Baer-invariant of finitely generated Abelian groups. Also, it is done for some non-Abelian groups, such the dihedral and the quaternion groups directly, and sometimes with the softwares of Gap and Magma. But nobody works on non finitely generated Abelian groups. In 1979, M.R.R. Moghaddarn showed that the structure of Baer-invariant of group commutes with the direct limit of a directed system, in some sense. The authors have used these results and proved that the Baer-invariant of C is always trivial and also Baer-invariant of Abelian groups Q/z and Z （p∞）, with respect to the varieties of outer commutators and so polynilpotent, nilpotent are trivial. One can see immediately that the covering groups of these groups are themselves. Then after computing the Baer-invariant of Zn with respect to Burnside variety, we have concluded for Q/z and Z（P∞） Burnside variety. In the future, they try to survey the commutativity of the Baer-invariant variety with the other useful varieties in order to attain similar results for another non finitely generated Abelian groups.展开更多
文摘Let g = W1 be the Witt algebra over an algebraically closed field k of characteristic p 〉 3, and let ∮（g） = {（x,y） ∈ g×g [x,y] = 0} be the commuting variety of g. In contrast with the case of classical Lie algebras of P. Levy [J. Algebra, 2002, 250： 473-484], we show that the variety ∮（g） is reducible, and not equidimensional. Irreducible components of ∮（g） and their dimensions are precisely given. As a consequence, the variety ∮（g） is not normal.
基金Supported by the National Natural Science Foundation of China (Grant No.10571077)the Natural Science Foundation of Gansu Province (Grant No.3ZS032-A25-017)
文摘In this paper, all subvarieties of the varieties Ak （k ∈N） generated by aperiodic commutative semigroups are characterized. Based on this characterization, the structure of lattice of subvarieties of Ak is investigated.
文摘Many of people have tried to obtain the structure of Baer-invariant of groups exactly. Recently, B. Mashayekhy and M. Parvizi determine Baer-invariant of finitely generated Abelian groups. Also, it is done for some non-Abelian groups, such the dihedral and the quaternion groups directly, and sometimes with the softwares of Gap and Magma. But nobody works on non finitely generated Abelian groups. In 1979, M.R.R. Moghaddarn showed that the structure of Baer-invariant of group commutes with the direct limit of a directed system, in some sense. The authors have used these results and proved that the Baer-invariant of C is always trivial and also Baer-invariant of Abelian groups Q/z and Z （p∞）, with respect to the varieties of outer commutators and so polynilpotent, nilpotent are trivial. One can see immediately that the covering groups of these groups are themselves. Then after computing the Baer-invariant of Zn with respect to Burnside variety, we have concluded for Q/z and Z（P∞） Burnside variety. In the future, they try to survey the commutativity of the Baer-invariant variety with the other useful varieties in order to attain similar results for another non finitely generated Abelian groups.
