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Noncommutative algebraic geometry.

Olav A. Laudal (2003)

Revista Matemática Iberoamericana

The need for a noncommutative algebraic geometry is apparent in classical invariant and moduli theory. It is, in general, impossible to find commuting parameters parametrizing all orbits of a Lie group acting on a scheme. When one orbit is contained in the closure of another, the orbit space cannot, in a natural way, be given a scheme structure. In this paper we shall show that one may overcome these difficulties by introducing a noncommutative algebraic geometry, where affine schemes are modeled...

Noncommutative Hodge-to-de Rham spectral sequence and the Heegaard Floer homology of double covers

Robert Lipshitz, David Treumann (2016)

Journal of the European Mathematical Society

Let A be a dg algebra over 𝔽 2 and let M be a dg A -bimodule. We show that under certain technical hypotheses on A , a noncommutative analog of the Hodge-to-de Rham spectral sequence starts at the Hochschild homology of the derived tensor product M ⊗ A L M and converges to the Hochschild homology of M . We apply this result to bordered Heegaard Floer theory, giving spectral sequences associated to Heegaard Floer homology groups of certain branched and unbranched double covers.

Non-commutative separability and group actions.

Ricardo Alfaro (1992)

Publicacions Matemàtiques

We give conditions for the skew group ring S * G to be strongly separable and H-separable over the ring S. In particular we show that the H-separability is equivalent to S being central Galois extension. We also look into the H-separability of the ring S over the fixed subring R under a faithful action of a group G. We show that such a chain: S * G H-separable over S and S H-separable over R cannot occur, and that the centralizer of R in S is an Azumaya algebra in the presence of a central element...

Nonlinear * -Lie higher derivations of standard operator algebras

Mohammad Ashraf, Shakir Ali, Bilal Ahmad Wani (2018)

Communications in Mathematics

Let ℋ be an infinite-dimensional complex Hilbert space and 𝔄  be a standard operator algebra on ℋ which is closed under the adjoint operation. It is shown that every nonlinear * -Lie higher derivation 𝒟 = { δ n } n ∈ ℕ of 𝔄 is automatically an additive higher derivation on 𝔄 . Moreover, 𝒟 = { δ n } n ∈ ℕ is an inner * -higher derivation.

Non-linear maps preserving ideals on a parabolic subalgebra of a simple algebra

Deng Yin Wang, Haishan Pan, Xuansheng Wang (2010)

Czechoslovak Mathematical Journal

Let 𝒫 be an arbitrary parabolic subalgebra of a simple associative F -algebra. The ideals of 𝒫 are determined completely; Each ideal of 𝒫 is shown to be generated by one element; Every non-linear invertible map on 𝒫 that preserves ideals is described in an explicit formula.

Nonlinear maps preserving Lie products on triangular algebras

Weiyan Yu (2016)

Special Matrices

In this paper we prove that every bijection preserving Lie products from a triangular algebra onto a normal triangular algebra is additive modulo centre. As an application, we described the form of bijections preserving Lie products on nest algebras and block upper triangular matrix algebras.

Currently displaying 41 – 60 of 99