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Title Quasi Quantum Groups and Monoidal Categories

Contract number 47/2022,

Project CNCSIS PN-III-P4_PCE-2021-0282 

 

Research team

  1. Daniel Bulacu (project leader)
  2. Sorin Dăscălescu (experienced researcher)
  3. Maria Joița (experienced researcher)
  4. Constantin Năstăsescu (experienced researcher)
  5. Florin Panaite (experienced researcher)
  6. Dragoş Ştefan (experienced researcher)
  7. Anca Niţă (master student)

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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.

 

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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

  1. D. Bulacu, B. Torrecillas, 1-Homology for coalgebras in Yetter-Drinfeld categories, submitted.
  2. D. Bulacu, D. Popescu, B. Torrecillas, Double wreath quasi-Hopf algebras, work in progress.
  3. S. Dăscălescu, C. Năstăsescu, L. Năstăsescu: Graded Frobenius rings, submitted.
  4. M. Joiţa, Finsler locally C*-modules, work in progress.
  5. L. Liu, A. Makhlouf, C. Menini, F. Panaite, BiHom-NS-algebras, twisted Rota-Baxter operators and generalized Nijenhuis operators, submitted.
  6. 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 

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

 

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Scientific and financial reports

2022

Scientific report

Post-calculation assessment

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