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Abstrakty
In [1, 2, 3], *-algebras and *-categories over the field C of complex numbers were quasi-ordered with respect to the complexity of the structure of their *-representations with a majorization relation >-. A notion of *-wildness was also introduced there for an algebra (a category) if the algebra majorizes the *-algebra C* (F2)- In this paper, we discuss some methods for proving that an algebra is *-wild and obtain criteria for certain "standard" *-categories (ensembles with an orthogonality condition) to be *-wild.
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Czasopismo
Rocznik
Tom
Strony
5--17
Opis fizyczny
Bibliogr. 6 poz.
Twórcy
autor
- Institute of Mathematics of the National Academy of Sciences of Ukraine, vul. Tereshchinkivs’ka, 3, Kyiv, 01601, Ukraine
autor
- Institute of Mathematics of the National Academy of Sciences of Ukraine, vul. Tereshchinkivs'ka 3, Kyiv, 01601, Ukraine
Bibliografia
- [1] Kruglyak S. A., Samoilenko Yu. S.: On structure theorems for a family of idempo-tents. Ukrainskii Matematicheskii Zhurnal 50(4), (1998) (Russian).
- [2] Kruglyak S. A., Samoilenko Yu. S.: On the complexity of description of representations of *-algebras generated by idempotents. [in:] Proc. ol the American Mathematical Society, vol. 128, 1655-1664, AMS, 2000.
- [3] Kruglyak S. A.: A majorization relation for ^-categories and *-wild categories, [in:] Proc. ol the Filth Intern. Conference "Symmetry in Nonlinear Math. Physics", 2004.
- [4] Roiter A. V.: Boxes with an involution, [in:] Representations and quadratic forms, Kiev, 1979, 124-126 (Russian).
- [5] Kruglyak S.A.: Representations of free involutive quivers, [in:] Representations and quadratic forms, Kiev, 1979, 149-151 (Russian).
- [6] Kruglyak S.A., Samoilenko Yu. S.: On unitary equivalence of collections of self-adjoint operators. Funct. Anal. Appl. 1980, 84-85, (Russian).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-AGH4-0005-0061