TY  - JOUR
ID  - Bagro2004
LB  - Bagro2004
AU  - Bagro, O. V.
AU  - Kruglyak, S. A.
TI  - A majorization relation for a certain class of *-quivers with an orthogonality condition
ST  - A majorization relation for a certain class of *-quivers with an orthogonality condition
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2004
VL  - 24
IS  - 1
SP  - 5
EP  - 17
DO  - http://dx.doi.org/10.7494/OpMath.2004.24.1.5
UR  - http://dx.doi.org/10.7494/OpMath.2004.24.1.5
AB  - In [Kruglyak S. A., Samoĭlenko Yu. S.: On structure theorems for a family of idempotents. Ukrainskii Matematicheskii Zhurnal 50 (4), (1998) (Russian), Kruglyak S. A., Samoĭlenko Yu. S.: On the complexity of description of representations of \(*\)-algebras generated by idempotents. [in:] Proc. of the American Mathematical Society, vol. 128, 1655–1664, AMS, 2000, Kruglyak S. A.: A majorization relation for \(*\)-categories and \(*\)-wild categories. [in:] Proc. of the Fifth Intern. Conference "Symmetry in Nonlinear Math. Physics", 2004], \(*\)-algebras and \(*\)-categories over the field \(\mathbb{C}\) of complex numbers were quasi-ordered with respect to the complexity of the structure of their \(*\)-representations with a majorization relation \(\succ\). A notion of \(*\)-wildness was also introduced there for an algebra (a category) if the algebra majorizes the \(*\)-algebra \(C^{*}(\mathcal{F}_2)\). 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.
KW  - algebras
KW  - categories and functors
KW  - representations
SN  - 1232-9274
ER  -