Other answers have already provided sufficient citations for Brahman is actionless, like Nishkalam Nishkriyam Shaantam Niravadyam Niranjanam (SvetUp- 6.19)
An action's relativity, and its continuity presupposes an actionless absolute Brahman (which Kenopanishad refers to).
Also ,श्रोत्रस्य श्रोत्रं , मनसो मनो यत् is One, This same idea is found in CU 6.2.1
sadeva somyedam agra āsīd ekamevādvitīyam | taddhaika āhurasadevedamagra āsīd ekamevādvitīyaṃ tasmādasataḥ sajjāyata || 6.2.1 ||
one without a second
so, how come this perception of Brāhmaṇa not being an active agent enter into the mind of later Advaitins, because it surely wasn't Śaṅkara's view at all.
(@Bingming, how is this reconciled?)
This may not be the case, as we find in several
Prakarana Granthas by Shankaracharya say, Atma bodha verse 37, Vivekachudamani 491
Nirguṇo niṣkriyo nityo nirvikalpo nirañjanaḥ.
Nirvikāro nirākāro nityamukto’smi nirmalaḥ..AB34..
Indeed, I am other than the seer, hearer, speaker, doer and Experiencer. I am eternal and unbroken,
beyond activity, boundless, unattached and infinite, the essence of knowledge. VC491
world is an effect of Brāhmaṇ
as in CU 6.1.4 could be the basis of Vivarta vada.
yathā somyaikena mṛtpiṇḍena sarvaṃ mṛnmayaṃ vijñātaṃ syādvācārambhaṇaṃ vikāro nāmadheyaṃ mṛttiketyeva satyam || 6.1.4 ||
O Somya, it is like this: By knowing a single lump of earth you know all objects made of earth. All changes are mere words, in name only. But earth is the reality.
vācārambhaṇam nāmadheyam vikāraḥ all changes are mere words, in name only; mṛttika iti eva satyam, the earth is the reality.
As there is no other entity other than Brahman, Brahman by whose inscrutable power Maya, appears as creation. It is understood as Vivarta Vada of Advaita.
All duality which Ś clearly declared to be merely imaginary (kalpita) now came to be viewed by his commentators as a very real and existent duality.
Vivekachudamani 109 says
Maya is neither existent nor non-existent nor partaking of both characters; neither same nor different nor both; neither composed of parts nor an indivisible whole nor both. She is the most wonderful and cannot be described in words.”
Maya (the word occurs in (Svet. Up 4.10)) the anirvachaniya (either real or non real), explained as part of BG 2.16, cannot be a second real entity, (Sat) so as to say real and existent duality.
Is Advaita refuted by Brahma Sutras?
It is as though the commentators were off the track, and fell in line with sankya (where Prakrithi is a separate entity other than Brahman, creates its own evolutes, with the power received from purusha who is non-attached to the creation).
In the perspective of Gita,
What does Actionlessness connote
कर्मण्यकर्म यः पश्येदकर्मणि च कर्म यः।
स बुद्धिमान् मनुष्येषु स युक्तः कृत्स्नकर्मकृत्।।
He who finds inaction in action, and action in inaction, he is the wise one [Possessed of the knowledge of Brahman] among men; he is engaged in yoga and is a performer of all actions! (Swami Gambirananda) BG 4.18
Shankaracharyas Commentary
the trees on the shore which are motionless? appear to move in the opposite direction to a man who is in traveling. Moving objects that are very far away appear to be stationary or motionless. Even so in the case of the Self inaction is mistaken for action and, action for inaction.The Self is actionless (Akarta or nondoer? Nishkriya or without work).
(Translation Swami Gambirananda)
In the context of the analogy, one is well aware of the absolute stand point (that the tree or the post does not move, though it appears so). In reality the absolute stand point is not known. Hence, it is hard to accept the action is an illusion.
न मां कर्माणि लिम्पन्ति न मे कर्मफले स्पृहा।
इति मां योऽभिजानाति कर्मभिर्न स बध्यते।।4.14।
Her , the omniscient Supreme reality, though creates sustains and dissolves the universe, identifies with the Self (Brahman), and not with the action (karma phale na sprha, there is no hankering for the results, hence not tainted by the action - karmani limpanti).
In the same way, the actions do not taint a Jiva (Actionlessness) who does not hanker for karma phala, by identifying with the action (rather who identifies with the self) and what follows is,
jñānāgniḥ sarva-karmāṇi bhasma-sāt kurute tathā