Scientific Objectives Budget
Research founded by the
project Scientific
seminar Financial
and Scientific Reports
Title Quasi Quantum Groups
and Monoidal Categories
Contract number 47/2022,
Project CNCSIS PN-III-P4_PCE-2021-0282
Research team
- Daniel Bulacu (project leader)
- Sorin Dăscălescu (experienced
researcher)
- Maria Joița (experienced researcher)
- Constantin Năstăsescu (experienced
researcher)
- Florin Panaite (experienced researcher)
- Dragoş Ştefan (experienced researcher)
- Anca Niţă (master student)
Scientific
objectives
There
are three work-packages:
1. New classes of
Frobenius-Lusztig kernels quasi quantum groups (qQGs for short)
2. Quasi-quantum
groups of Nichols type and quasi-quantum shuffle groups and
3. Modular categories defined by quasi-quantum groups and related
structures.
The objectives
corresponding to them are:
1. The structure of a
qQG with a coalgebra projection, the construction of the quasi-Hopf analogue of
U_qg and of the Frobenius-Lusztig kernels for qQGs, and to provide a
generalization for the L-R-crossed products that contains a 2-cocycle
deformation of a double-biproduct as a particular case;
2. Determine the
braided tensor Hopf algebras corresponding to certain qQGs as well as some
quotients of them, characterize shuffle qQGs in categories of Hopf bimodules as
biproduct quasi-Hopf algebras and obtain examples from abelian groups,
universal Clifford algebras and universal (quasi) quantum groups;
3. Find conditions under which YD-modules over a qQG H is balanced and respectively
ribbon, determine when a quasi-quantum double D(H) is ribbon and interpret the
obtained results in terms of H, and the study of the possible connections
between finite (co)wreaths with the associated category of (co)representations
monoidal/sovereign/braided/spherical/ modular and some properties of the
(co)algebra in the Eilenberg-Moore category associated to the (co)wreath.
Budget
|
NR. CRT.
|
DENUMIRE CAPITOL BUGET
|
2022
|
2023
|
2024
|
TOTAL
|
|
1
|
PERSONEL
EXPENSES
|
143.530
|
322.900
|
322.885
|
789.315
|
|
2
|
INDIRECT
EXPENSES
|
25.674
|
63.492
|
61.485
|
150.651
|
|
3
|
TRAVEL
EXPENSES
|
24.618
|
95.382
|
80.000
|
200.000
|
|
4
|
LOGISTIC
EXPENSES
|
33.010
|
20.000
|
7.015
|
60.025
|
|
5
|
TOTAL
|
226.832
|
501.774
|
471.385
|
1.199.991
|
Up
Research
funded by this project
2022
- D.
Bulacu, B. Torrecillas, 1-Homology for coalgebras in Yetter-Drinfeld
categories, submitted.
- D.
Bulacu, D. Popescu, B. Torrecillas, Double wreath quasi-Hopf algebras,
work in progress.
- S.
Dăscălescu, C. Năstăsescu, L. Năstăsescu:
Graded Frobenius rings, submitted.
- M.
Joiţa, Finsler locally C*-modules, work in progress.
- L. Liu,
A. Makhlouf, C. Menini, F. Panaite, BiHom-NS-algebras, twisted Rota-Baxter
operators and generalized Nijenhuis operators, submitted.
- A.
Makhlouf, D. Ștefan, Deformations of algebraic structures in monoidal
categories, work in progress.
Up
Scientific
seminar
|
Topic
|
Data
|
Time
|
Room
|
|
Reconstruction theorems
|
3.11.2022
|
12-14
|
309
|
|
Reconstruction theorems
|
10.11.2022
|
12-14
|
309
|
|
C* algebras
|
17.11.2022
|
12-14
|
309
|
|
C* algebras
|
24.11.2022
|
12-14
|
309
|
|
C* algebras
|
8.12.2022
|
12-14
|
309
|
|
C* algebras
|
15.12.2022
|
12-14
|
309
|
Up
Scientific and
financial reports
2022
Scientific report
Post-calculation
assessment
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