Öz
Kaynakça
- H. H. Andersen and V. Mazorchuk, Category $\O$ for quantum groups, J. Eur. Math. Soc. (JEMS), 17(2) (2015), 405-431.
- J. E. Humphreys, Representations of semisimple Lie algebras in the BGG category $\O$, Grad. Stud. Math., American Math. Soc., 94, 2008.
- R. Kane, Reflection Groups and Invariant Theory, CMS Books Math./Ouvrages Math. SMC, 5, Springer-Verlag, New York, 2001.
- C. Voigt and R. Yuncken, Complex semisimple quantum groups and representation theory, Lecture Notes in Math., 2264, Springer, Cham, 2020.
- Z. Wei, Tensor-closed objects in the BGG category of a quantized semisimple Lie algebra, Int. Electron. J. Algebra, 29 (2021), 175-186.
Tensor products of infinite dimensional modules in the BGG category of a quantized simple Lie algebra of type ADE
Öz
We consider the BGG category $\O$ of a quantized universal enveloping algebra $U_q(\mathfrak{g})$. It is well-known that $M\otimes N\in \O$ if $M$ or $N$ is finite dimensional. When $\mathfrak{g}$ is simple and of type ADE, we prove in this paper that $M\otimes N\notin \O$ if $M$ and $N$ are both infinite dimensional.
Anahtar Kelimeler
BGG category quantized universal enveloping algebra tensor product formal character
Kaynakça
- H. H. Andersen and V. Mazorchuk, Category $\O$ for quantum groups, J. Eur. Math. Soc. (JEMS), 17(2) (2015), 405-431.
- J. E. Humphreys, Representations of semisimple Lie algebras in the BGG category $\O$, Grad. Stud. Math., American Math. Soc., 94, 2008.
- R. Kane, Reflection Groups and Invariant Theory, CMS Books Math./Ouvrages Math. SMC, 5, Springer-Verlag, New York, 2001.
- C. Voigt and R. Yuncken, Complex semisimple quantum groups and representation theory, Lecture Notes in Math., 2264, Springer, Cham, 2020.
- Z. Wei, Tensor-closed objects in the BGG category of a quantized semisimple Lie algebra, Int. Electron. J. Algebra, 29 (2021), 175-186.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Cebir ve Sayı Teorisi, Grup Teorisi ve Genellemeler, Kategori Teorisi, K Teorisi, Homolojik Cebir, Temel Matematik (Diğer) |
| Bölüm | Makaleler |
| Yazarlar | |
| Erken Görünüm Tarihi | 8 Eylül 2023 |
| Yayımlanma Tarihi | 9 Ocak 2024 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 35 Sayı: 35 |