TY  - BOOK
AU  - Giri, Manabendra
TI  - Crystallization of the quantized function algebras of SUq(n + 1)
U1  - 512.556 23rd
PY  - 2025///
CY  - Delhi
PB  - Indian Statistical Institute
KW  - Mathematics
KW  - Quantized Function Algebras
KW  - Quantum Groups
KW  - q-deformation
N1  - Thesis (Ph.D) - Indian Statistical Institute, 2025; Includes bibliography; Introduction -- Preliminaries -- The crystalized C∗-algebra -- Irreducible representations of C(SU0(3)) -- Irreducible representations of C(SU0(n + 1)); Guided by Prof. Arup Kumar Pal
N2  - The $q$-deformation of a connected, simply connected Lie group $G$ is typically studied through two Hopf algebras associated with it: the quantized universal enveloping algebra $\mathcal{U}_q(\mathfrak{g})$ and the quantized function algebra $\mathcal{O}(G_q)$. If $G$ has a compact real form $K$, one can use the Cartan involution to give a $*$-structure on $\mathcal{O}(G_q)$. The QFA $\mathcal{O}(G_q)$ with this $*$ structure is denoted by $\mathcal{O}(K_q)$ and its $C^*$-completion by $C(K_q)$. Here we study the crystal limits of $\mathcal{O}(SU_q(n+1))$ and $C(SU_q(n+1))$ and classify all irreducible representations of the crystallized algebras. We also prove that the crystallized algebra carries a natural bialgebra structure
UR  - https://dspace.isical.ac.in/jspui/handle/10263/7553
ER  -