Bedratyuk, Leonid (2010)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 13N15, 13A50, 16W25. By using classical invariant theory approach, formulas for computation of the Poincaré series of the kernel of linear locally nilpotent derivations are found.
Bedratyuk, Leonid (2011)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 13N15, 13A50, 13F20. An analogue of the symbolic method of classical invariant theory for a representation and manipulation of the elements of the kernel of Weitzenböck derivations is developed.
Qimei Xiao, Wenjun Liu (2016)
Open Mathematics
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A quantale is a complete lattice equipped with an associative binary multiplication distributing over arbitrary joins. We define the notions of right (left, two) sided derivation and idempotent derivation and investigate the properties of them. It’s well known that quantic nucleus and quantic conucleus play important roles in a quantale. In this paper, the relationships between derivation and quantic nucleus (conucleus) are studied via introducing the concept of pre-derivation. ...
Benjamin Audoux (2014)
Winter Braids Lecture Notes
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These notes were written for a series of lectures on the Rasmussen invariant and the Milnor conjecture, given at Winter Braids IV in February 2014.
Martin Mathieu (1994)
Banach Center Publications
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With this paper, we intend to provide an overview of some recent work on a problem on unbounded derivations of Banach algebras that still defies solution, the non-commutative Singer-Wermer conjecture. In particular, we discuss several global as well as local properties of derivations entailing quasinilpotency in the image.
Yan, Dangui, Zhang, Chengchang (2011)
International Journal of Mathematics and Mathematical Sciences
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Matthew J. Heath (2010)
Banach Center Publications
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We consider the compactness of derivations from commutative Banach algebras into their dual modules. We show that if there are no compact derivations from a commutative Banach algebra, A, into its dual module, then there are no compact derivations from A into any symmetric A-bimodule; we also prove analogous results for weakly compact derivations and for bounded derivations of finite rank. We then characterise the compact derivations from the convolution algebra ℓ¹(ℤ₊) to its dual. Finally,...
Gerard Murphy (1994)
Banach Center Publications
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We survey some old and new results in the theory of derivations on Banach algebras. Although our overview is broad ranging, our principal interest is in recent results concerning conditions on a derivation implying that its range is contained in the radical of the algebra.
V. Shul'Man (1994)
Studia Mathematica
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The aim of this paper is to prove that derivations of a C*-algebra A can be characterized in the space of all linear continuous operators T : A → A by the conditions T(1) = 0, T(L∩R) ⊂ L + R for any closed left ideal L and right ideal R. As a corollary we get an extension of the result of Kadison [5] on local derivations in W*-algebras. Stronger results of this kind are proved under some additional conditions on the cohomologies of A.
Utkina, E.A. (2005)
Lobachevskii Journal of Mathematics
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Jan von Plato (2017)
Bulletin of the Section of Logic
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The way from linearly written derivations in natural deduction, introduced by Jaskowski and often used in textbooks, is a straightforward root-first translation. The other direction, instead, is tricky, because of the partially ordered assumption formulas in a tree that can get closed by the end of a derivation. An algorithm is defined that operates alternatively from the leaves and root of a derivation and solves the problem.
Barrenechea, A.L., Peña, C.C. (2005)
Lobachevskii Journal of Mathematics
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Ben Yakoub, L., Louly, A. (2009)
Beiträge zur Algebra und Geometrie
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Martin Weigt, Ioannis Zarakas (2015)
Studia Mathematica
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We show that every continuous derivation of a countably dominated Fréchet GB*-algebra A is spatial whenever A is additionally an AO*-algebra.
Gene Freudenburg (2001)
Annales Polonici Mathematici
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We give an overview of recent results concerning kernels of triangular derivations of polynomial rings. In particular, we examine the question of finite generation in dimensions 4, 5, 6, and 7.
P. G. Dodds, E. M. Semenov, F. A. Sukochev (2002)
Studia Mathematica
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We present necessary and sufficient conditions for a rearrangement invariant function space to have a complete orthonormal uniformly bounded RUC system.
O. Bratteli, G. A. Elliott, P. E. T. Jorgensen (1984)
Journal für die reine und angewandte Mathematik
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K. Beidar, Matej Brešar (2000)
Studia Mathematica
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The problem of when derivations (and their powers) have the range in the Jacobson radical is considered. The proofs are based on the density theorem for derivations.
Amir Hosein Mokhtari, Fahimeh Moafian, Hamid Reza Ebrahimi Vishki (2017)
Annales Mathematicae Silesianae
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In this paper we provide some conditions under which a Lie derivation on a trivial extension algebra is proper, that is, it can be expressed as a sum of a derivation and a center valued map vanishing at commutators. We then apply our results for triangular algebras. Some illuminating examples are also included.