Derived equivalences and higher \(K\)-groups of a class of KLR algebras. (English) Zbl 1448.18023
Summary: For a Khovanov-Lauda-Rouquier algebra \(\mathcal K\) defined by an unoriented graph of type \(A_n\), we prove that \(\mathcal K\) is derived equivalent to a matrix-like algebra \(\mathcal T.\) Under this equivalence, the higher \(K\)-groups and global dimension of \(\mathcal K\) have been described.
MSC:
| 18G80 | Derived categories, triangulated categories |
| 16G10 | Representations of associative Artinian rings |
| 13B30 | Rings of fractions and localization for commutative rings |
| 16S10 | Associative rings determined by universal properties (free algebras, coproducts, adjunction of inverses, etc.) |
| 16E35 | Derived categories and associative algebras |
| 13F05 | Dedekind, Prüfer, Krull and Mori rings and their generalizations |
| 16D90 | Module categories in associative algebras |
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