Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Categorifying fractional Euler characteristics, Jones-Wenzl projector
  and $3j$-symbols   We study the representation theory of the smallest quantum group and its
categorification. The first part of the paper contains an easy visualization of
the 3j-symbols in terms of weighted signed line arrangements in a fixed
triangle and new binomial expressions for the 3j-symbols. All these formulas
are realized as graded Euler characteristics. The 3j-symbols appear as new
generalizations of Kazhdan-Lusztig polynomials. A crucial result of the paper
is that complete intersection rings can be employed to obtain rational Euler
characteristics, hence to categorify rational quantum numbers. This is the main
tool for our categorification of the Jones-Wenzl projector, Theta-networks and
tetrahedron networks. Networks and their evaluations play an important role in
the Turaev-Viro construction of 3-manifold invariants, \cite{TV}. We categorify
these evaluations by Ext-algebras of certain simple Harish-Chandra bimodules.
The relevance of this construction to categorified colored Jones invariants and
invariants of 3-manifolds will be studied in detail in subsequent papers.

31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga