A majorization relation for a certain class of *-quivers with an orthogonality condition

• Autorzy: Bagro O.V. , Kruglyak S.A.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

algebras; categories and functors; representations

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2004
• Tom: Vol. 24, no. 1
• Strony: 5--17
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Bagro O.V.

• Institute of Mathematics of the National Academy of Sciences of Ukraine, vul. Tereshchinkivs’ka, 3, Kyiv, 01601, Ukraine

autor

Kruglyak S.A.

• 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).