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 PNIIIP4_PCE20210282
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 workpackages:
1. New classes of
FrobeniusLusztig kernels quasi quantum groups (qQGs for short)
2. Quasiquantum
groups of Nichols type and quasiquantum shuffle groups and
3. Modular categories defined by quasiquantum groups and related
structures.
The objectives
corresponding to them are:
1. The structure of a
qQG with a coalgebra projection, the construction of the quasiHopf analogue of
U_qg and of the FrobeniusLusztig kernels for qQGs, and to provide a
generalization for the LRcrossed products that contains a 2cocycle
deformation of a doublebiproduct 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 quasiHopf algebras and obtain examples from abelian groups,
universal Clifford algebras and universal (quasi) quantum groups;
3. Find conditions under which YDmodules over a qQG H is balanced and respectively
ribbon, determine when a quasiquantum 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 EilenbergMoore 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

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Research
funded by this project
2022
 D.
Bulacu, B. Torrecillas, 1Homology for coalgebras in YetterDrinfeld
categories, submitted.
 D.
Bulacu, D. Popescu, B. Torrecillas, Double wreath quasiHopf 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, BiHomNSalgebras, twisted RotaBaxter
operators and generalized Nijenhuis operators, submitted.
 A.
Makhlouf, D. Ștefan, Deformations of algebraic structures in monoidal
categories, work in progress.
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Scientific
seminar
Topic

Data

Time

Room

Reconstruction theorems

3.11.2022

1214

309

Reconstruction theorems

10.11.2022

1214

309

C* algebras

17.11.2022

1214

309

C* algebras

24.11.2022

1214

309

C* algebras

8.12.2022

1214

309

C* algebras

15.12.2022

1214

309

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Scientific and
financial reports
2022
Scientific report
Postcalculation
assessment
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