Öz
We consider the BGG category $\O$ of a quantized universal
enveloping algebra $U_q(\mathfrak{g})$. We call a module $M\in
\O$ tensor-closed if $M\otimes N\in\O$ for any $N\in \O$. In this
paper we prove that $M\in \O$ is tensor-closed if and only if $M$
is finite dimensional. The method used in this paper applies to
the unquantized case as well.
Anahtar Kelimeler
BGG category quantized universal enveloping algebra tensor product formal character
Kaynakça
- H. H. Andersen and V. Mazorchuk, Category $\mathscr{O}$ for quantum groups, J. Eur. Math. Soc., 17(2) (2015), 405-431.
- J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Second printing, revised, Graduate Texts in Mathematics, 9, Springer-Verlag, New York-Berlin, 1978.
- J. E. Humphreys, Representations of Semisimple Lie Algebras in the BGG Category $\mathscr{O}$, Graduate Studies in Mathematics, 94, American Mathematical Society, Providence, RI, 2008.
- J. E. Humphreys, Tensor-closed objects of the BGG category $\mathscr{O}$, (2015), Preprint available on the author's website: http://people.math.umass.edu / jeh/pub/ tensor.pdf.
- A. Joseph, Quantum Groups and Their Primitive Ideals, Ergebnisse der Mathematik und ihrer Grenzgebiete, (3) 29, Springer-Verlag, Berlin, 1995.
- V. A. Lunts and A. L. Rosenberg, Localization for quantum groups, Selecta Math. (N.S.), 5(1) (1999), 123-159.
- C. Voigt and R. Yuncken, Complex semisimple quantum groups and representation theory, (2017), arXiv:1705.05661.
- Z. Wei, Tensor products of infinite dimensional modules in the BGG category of a quantized simple Lie algebra of type ADE, (2019), Preprint available on the author's website: https://drive.google.com/file/d/1ZogGH4Rfenq7AXTvxOdsoqGbSHCbfrjr/view.
- Z. Wei, Tensor products of infinite dimensional modules in the BGG category of a quantized simple Lie algebra of type ADE, (2019), Preprint available on the author's website: https://drive.google.com/file/d/1ZogGH4Rfenq7AXTvxOdsoqGbSHCbfrjr/view.
Öz
Kaynakça
- H. H. Andersen and V. Mazorchuk, Category $\mathscr{O}$ for quantum groups, J. Eur. Math. Soc., 17(2) (2015), 405-431.
- J. E. Humphreys, Introduction to Lie Algebras and Representation Theory, Second printing, revised, Graduate Texts in Mathematics, 9, Springer-Verlag, New York-Berlin, 1978.
- J. E. Humphreys, Representations of Semisimple Lie Algebras in the BGG Category $\mathscr{O}$, Graduate Studies in Mathematics, 94, American Mathematical Society, Providence, RI, 2008.
- J. E. Humphreys, Tensor-closed objects of the BGG category $\mathscr{O}$, (2015), Preprint available on the author's website: http://people.math.umass.edu / jeh/pub/ tensor.pdf.
- A. Joseph, Quantum Groups and Their Primitive Ideals, Ergebnisse der Mathematik und ihrer Grenzgebiete, (3) 29, Springer-Verlag, Berlin, 1995.
- V. A. Lunts and A. L. Rosenberg, Localization for quantum groups, Selecta Math. (N.S.), 5(1) (1999), 123-159.
- C. Voigt and R. Yuncken, Complex semisimple quantum groups and representation theory, (2017), arXiv:1705.05661.
- Z. Wei, Tensor products of infinite dimensional modules in the BGG category of a quantized simple Lie algebra of type ADE, (2019), Preprint available on the author's website: https://drive.google.com/file/d/1ZogGH4Rfenq7AXTvxOdsoqGbSHCbfrjr/view.
- Z. Wei, Tensor products of infinite dimensional modules in the BGG category of a quantized simple Lie algebra of type ADE, (2019), Preprint available on the author's website: https://drive.google.com/file/d/1ZogGH4Rfenq7AXTvxOdsoqGbSHCbfrjr/view.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 5 Ocak 2021 |
| Yayımlandığı Sayı | Yıl 2021 Cilt: 29 Sayı: 29 |